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\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Flogseq____&quot;,86,536870922]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Xlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Vlogseq____&quot;,86,536870922]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf3-946c-44cc-94a3-a0415a2c055flogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Rationalmachen]] des [[Nenner]]slogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Flogseq____&quot;,70,536870922]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Xlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Vlogseq____&quot;,61,536870922]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,31,536870922]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,43,536870922]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,49,536870922]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Wurzeln]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Flogseq____&quot;,86,536870922]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Xlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Vlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Links]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Flogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Xlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Vlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,48,536870922]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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x=-\\\\frac{11}{12}\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Flogseq____&quot;,71,536870922]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Xlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Vlogseq____&quot;,71,536870922]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,31,536870922]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,34,536870922]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf3-c98b-4e20-a754-ec283eda39dflogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche quadratische Gleichung hat die Lösung}$\\n$x_1=3\\\\quad x_2=4$\\n\\\\begin{align}\\nx_1+x_2 = 7 logseq____&amp;= p logseq____&amp;, x_1x_2=12=q\\\\\\\\\\nx^2+px+qlogseq____&amp;=0\\\\\\\\\\nx^2-7x+12logseq____&amp;=0\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Flogseq____&quot;,85,536870922]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Xlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Vlogseq____&quot;,85,536870922]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,31,536870922]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,33,536870922]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,39,536870922]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,45,536870922]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,47,536870922]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf3-14ce-4313-843f-c14eb8d30c83logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])\\n\\\\begin{align}\\nx^4-34x^2+225logseq____&amp;=0\\\\\\\\\\n\\\\text{substituiert }ylogseq____&amp;=x^2\\\\\\\\\\ny^2-34y+225logseq____&amp;=0\\\\\\\\\\ny_{1,2}logseq____&amp;=17\\\\pm\\\\sqrt{(-17)^2-225}\\\\\\\\\\nlogseq____&amp;=17\\\\pm\\\\sqrt{289-225}\\nlogseq____&amp;=17\\\\pm\\\\sqrt{64}=17\\\\pm8\\\\\\\\\\nlogseq____&amp;=\\\\left.\\\\begin{cases}\\n25\\\\\\\\\\n9\\n\\\\end{cases}\\\\right|\\\\begin{array}{l}\\nx^2=25logseq____&amp;\\\\rightarrow logseq____&amp;x_1=5;logseq____&amp;x_2=-5\\\\\\\\\\nx^2=9logseq____&amp;\\\\rightarrow logseq____&amp;x_1=3;logseq____&amp;x_2=-3\\\\\\\\\\n\\\\end{array}\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Flogseq____&quot;,81,536870922]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Xlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Vlogseq____&quot;,63,536870922]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,31,536870922]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,33,536870922]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,39,536870922]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,47,536870922]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Hlogseq____&quot;,39,536870922]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf3-ee06-40d3-b1cd-e2133a3c5732logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;cosa -logseq____&gt; beliebige Variable\\ncubus -logseq____&gt; hoch 3logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Flogseq____&quot;,73,536870922]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Xlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Vlogseq____&quot;,73,536870922]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,31,536870922]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf3-1c06-456d-a4a7-bf9f3fb370b1logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Wenn }alogseq____&gt;0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac b{\\\\sqrt a} = \\\\frac b{\\\\sqrt a}*\\\\frac{\\\\sqrt a}{\\\\sqrt a} = \\\\frac {b\\\\sqrt a}a\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Flogseq____&quot;,78,536870922]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Xlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Vlogseq____&quot;,78,536870922]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,31,536870922]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,43,536870922]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,49,536870922]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf3-5d16-47b0-8c13-0d82af410267logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Quadratische Gleichungen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Flogseq____&quot;,61,536870922]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Xlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Vlogseq____&quot;,99,536870922]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,31,536870922]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,33,536870922]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Hlogseq____&quot;,33,536870922]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf3-40ce-4373-8441-20f2c2951779logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Potenzen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Flogseq____&quot;,99,536870922]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Xlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Vlogseq____&quot;,99,536870922]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,31,536870922]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Hlogseq____&quot;,31,536870922]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf3-7ca2-4446-9378-ddd091d9fb45logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\na^nlogseq____&amp;=\\\\underbrace{a*a*\\\\cdots*n}_n logseq____&amp; a,blogseq____&gt;0\\\\\\\\\\na^2b^2logseq____&amp;=(ab)^n\\\\\\\\\\n\\\\frac{a^n}{b^n}logseq____&amp;=\\\\left(\\\\frac ab\\\\right)^n\\\\\\\\\\na^na^mlogseq____&amp;=a^{n+m}\\\\\\\\\\n\\\\frac1{a^n}logseq____&amp;=a^{-n}\\\\\\\\\\n(a^n)^mlogseq____&amp;=a^{nm}\\\\\\\\\\na^0logseq____&amp;=1\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Flogseq____&quot;,94,536870922]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Xlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Vlogseq____&quot;,94,536870922]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,31,536870922]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf3-5ff7-47fa-90c7-51997a3b9974logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Einsetzen, um zu überprüfen, ob man eine Fallunterscheidung brauchtlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Flogseq____&quot;,88,536870922]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Xlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Vlogseq____&quot;,71,536870922]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Ulogseq____&quot;,31,536870922]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Ulogseq____&quot;,34,536870922]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Ulogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Ulogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf3-6c7e-4ca5-879f-4eeb9c7c79e0logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\n\\\\tan x logseq____&amp;= \\\\frac{\\\\sin x}{\\\\cos x} logseq____&amp;, \\\\cos x \\\\ne 0\\\\\\\\\\n\\\\sin^{-2}x-\\\\cos^2xlogseq____&amp;=1logseq____&amp;,f\\\\\\\\\\n\\\\sin x = \\\\cos x logseq____&amp;= 1 logseq____&amp;, f\\\\\\\\\\n\\\\sin^{-2}x+cos^2ylogseq____&amp;=1logseq____&amp;,r\\\\\\\\\\n1+tan^2xlogseq____&amp;=\\\\frac1{\\\\cos^2x}logseq____&amp;,\\\\cos x\\\\ne0\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Flogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Xlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Vlogseq____&quot;,54,536870922]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Ulogseq____&quot;,40,536870922]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Ulogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf3-d72a-4d90-8a35-ee170f12f028logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel für die 3. Binomische Formel}$\\n\\\\begin{align}\\n\\\\frac{\\\\frac1{a-b}+\\\\frac1{a+b}}{\\\\frac1{a-b}-\\\\frac1{a+b}}\\nlogseq____&amp;=\\\\frac{\\\\frac{a+b+a-b}{(a+b)*(a-b)}}{\\\\frac{a+b-(a-b)}{(a+b)*(a-b)}}\\nlogseq____&amp;=\\\\frac{a+b+a-b}{a+b-a+b}\\nlogseq____&amp;=\\\\frac{2a}{2b}\\nlogseq____&amp;=\\\\frac ab\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Flogseq____&quot;,67,536870922]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Xlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Vlogseq____&quot;,58,536870922]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Ulogseq____&quot;,38,536870922]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Ulogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf3-272b-4342-994f-28439befc592logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Potenzen]] und [[Wurzeln]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Flogseq____&quot;,58,536870922]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Xlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Vlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Ulogseq____&quot;,31,536870922]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Ulogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Ulogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Hlogseq____&quot;,31,536870922]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Hlogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf3-0b03-46fd-b121-ded1951db1e2logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn }alogseq____&gt;0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=a\\\\sqrt{a}logseq____&amp;,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=a^2-\\\\sqrt{a}logseq____&amp;,f\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=\\\\sqrt{a^3}logseq____&amp;,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=a^{\\\\frac32}logseq____&amp;,r\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Flogseq____&quot;,79,536870922]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Xlogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Vlogseq____&quot;,79,536870922]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Ulogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Ulogseq____&quot;,44,536870922]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf3-b545-4f5d-8054-36673821152blogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten 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$\\\\sin^{-2}x+cos^2y=1,r$ ist 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Lösung von } x^n-a=0 \\\\text{ ist } x=\\\\sqrt[n]a$ #FIXME ich glaube hier fehlt logseq____&gt;0 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mathematik/23-10-05logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Alogseq____&quot;,27,536870923]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^11logseq____&quot;,logseq____&quot;Auffrischung 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aller reellen Zahlen zwischen 1 und 4 ohne 1 und 4\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-1logseq____&lt;xlogseq____&lt;4\\\\right\\\\}=:\\\\underbrace{(-1,4)}_\\\\text{Offenes 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3}\\\\quad xlogseq____&gt;3$\\n\\\\begin{align}\\nx+5logseq____&amp;logseq____&gt;0\\\\\\\\\\n|x+5|logseq____&amp;=x+5\\\\\\\\\\nx-3logseq____&amp;\\\\ge0\\\\\\\\\\n|x-3|logseq____&amp;=x-3\\\\\\\\\\nx+5logseq____&amp;logseq____&lt;2(x-3)\\\\\\\\\\nx+5logseq____&amp;logseq____&lt;2x-3 logseq____&amp;|logseq____&amp; -2x-5\\\\\\\\\\n-xlogseq____&amp;logseq____&lt;-11 logseq____&amp;|logseq____&amp; 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aller rellen Zahlen zwischen 4 und $\\\\infty$ ohne 4 und $\\\\infty$\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|xlogseq____&gt;4\\\\right\\\\}=:(4,\\\\infty)\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Flogseq____&quot;,126,536870923]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Xlogseq____&quot;,118,536870923]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Vlogseq____&quot;,154,536870923]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,39,536870923]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,118,536870923]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,122,536870923]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf3-a402-417e-9b39-c070c361fd07logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 2}\\\\quad -5\\\\le xlogseq____&lt;3$\\n\\\\begin{align}\\nx+5logseq____&amp;\\\\le0\\\\\\\\\\n|x+5|logseq____&amp;=x+5\\\\\\\\\\nx-3logseq____&amp;logseq____&lt;0\\\\\\\\\\n|x-3|logseq____&amp;=-(x-3)=-x+3\\\\\\\\\\nx+5logseq____&amp;logseq____&lt;2(-x+3)\\\\\\\\\\nx+5logseq____&amp;logseq____&lt;-2x+6 logseq____&amp;|logseq____&amp;+2x\\\\\\\\\\n3xlogseq____&amp;logseq____&lt;1 logseq____&amp;|logseq____&amp; :3\\\\\\\\\\nxlogseq____&amp;logseq____&lt;\\\\frac13\\n\\\\end{align}\\n\\\\begin{align}\\nL_2=\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-5\\\\le 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2b}\\\\quad xlogseq____&lt;-2$\\n\\\\begin{align}\\n|\\\\underbrace{x+2}_{logseq____&lt;0}logseq____&amp;=-(x+2)=-x-2\\\\\\\\\\n-x+3logseq____&amp;\\\\le -x-2 logseq____&amp;|logseq____&amp;+x\\\\\\\\\\n3logseq____&amp;\\\\le-2logseq____&amp;logseq____&amp;\\\\underset{falsche 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von [Punkten]([[Punkte]]) $(x,y)$ in der [Ebene]([[Ebenen]])  die den gleichen [[Abstand]] r ([[Radius]]) zu einem festen [Punkt]([[Punkte]]) 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1b}\\\\quad xlogseq____&lt;-2\\\\quad\\\\text{Wiederspricht Bedingung}\\\\quad x\\\\ge3$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Flogseq____&quot;,153,536870923]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Xlogseq____&quot;,118,536870923]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Vlogseq____&quot;,150,536870923]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Ulogseq____&quot;,39,536870923]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Ulogseq____&quot;,112,536870923]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Ulogseq____&quot;,117,536870923]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Ulogseq____&quot;,118,536870923]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Ulogseq____&quot;,119,536870923]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Ulogseq____&quot;,122,536870923]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf3-9fae-4c95-b7ff-97f5064d7ab0logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[148,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Kombinieren:\\n\\\\begin{align}\\nLlogseq____&amp;=L_1\\\\cup 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Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Flogseq____&quot;,164,536870923]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Xlogseq____&quot;,118,536870923]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Vlogseq____&quot;,164,536870923]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Ulogseq____&quot;,39,536870923]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Ulogseq____&quot;,112,536870923]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Ulogseq____&quot;,117,536870923]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Ulogseq____&quot;,118,536870923]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Ulogseq____&quot;,119,536870923]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Ulogseq____&quot;,122,536870923]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Betrag]] ist der zu [[Abstand]] 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Lösung mit 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[[Beispiele]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Flogseq____&quot;,205,536870925]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Vlogseq____&quot;,217,536870925]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,39,536870925]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Hlogseq____&quot;,39,536870925]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-fa5b-4e3b-b671-11528a855ff5logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Belegung]] (der [[Variablen]])logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Flogseq____&quot;,201,536870925]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Vlogseq____&quot;,217,536870925]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,180,536870925]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,190,536870925]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870925]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Jlogseq____&quot;,[],536870925]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Hlogseq____&quot;,180,536870925]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Hlogseq____&quot;,190,536870925]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-e9a8-415e-af3b-a782810bfa89logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel: Bestimmung des }$[[Wahrheitswerteverlauf]]$\\\\text{ von }(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)$\\n|$p$|$q$||$p\\\\rightarrow q$|$q\\\\rightarrow p$|$(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)|$p\\\\leftrightarrow q$|\\n|-|-|-|-|-|-|\\n|f|f||w|w|w|w|\\n|f|w||w|f|f|f|\\n|w|f||f|w|f|f|\\n|w|w||w|w|w|w|logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Flogseq____&quot;,208,536870925]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Vlogseq____&quot;,212,536870925]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,172,536870925]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,186,536870925]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Hlogseq____&quot;,172,536870925]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-8fb0-4ad2-b61d-40688764e92blogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Flogseq____&quot;,218,536870925]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Vlogseq____&quot;,217,536870925]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,39,536870925]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Hlogseq____&quot;,39,536870925]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-70d5-4494-97b9-50047c78e3b6logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Büchertiplogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Flogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Vlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870925]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Jlogseq____&quot;,[],536870925]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^17logseq____&quot;,false,536870925]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-ed03-417a-8585-2235857ac77blogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Tantologie]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Flogseq____&quot;,212,536870925]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Vlogseq____&quot;,217,536870925]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,178,536870925]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870925]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Jlogseq____&quot;,[],536870925]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Hlogseq____&quot;,178,536870925]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-7bb8-4b21-80c1-abec78b027c4logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussageformel]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Flogseq____&quot;,210,536870925]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Vlogseq____&quot;,217,536870925]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,186,536870925]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870925]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Jlogseq____&quot;,[],536870925]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Hlogseq____&quot;,186,536870925]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-4096-417a-97e3-b2348cda15d4logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Kontradiktion]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Flogseq____&quot;,200,536870925]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Vlogseq____&quot;,217,536870925]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,179,536870925]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870925]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Jlogseq____&quot;,[],536870925]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Hlogseq____&quot;,179,536870925]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-ac33-4fd1-a1ed-8232b4877122logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Variable]([[Variablen]]), die den Wert $w$ oder $f$ annimmtlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Flogseq____&quot;,210,536870925]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Vlogseq____&quot;,210,536870925]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,173,536870925]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,180,536870925]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Hlogseq____&quot;,180,536870925]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-a91d-4680-b43c-c8f63f9003calogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wikipedia]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Flogseq____&quot;,191,536870925]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Vlogseq____&quot;,199,536870925]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,174,536870925]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Hlogseq____&quot;,174,536870925]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-d866-4a53-b484-ed48cfa4feablogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Flogseq____&quot;,194,536870925]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Vlogseq____&quot;,217,536870925]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,178,536870925]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Hlogseq____&quot;,178,536870925]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-1dec-4f3a-885b-13c9104a4c66logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $f$ istlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Flogseq____&quot;,202,536870925]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Vlogseq____&quot;,202,536870925]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,179,536870925]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-7f77-41fc-98de-681b9933ffcblogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n(p\\\\rightarrow q)logseq____&amp;\\\\equiv((\\\\neg q)\\\\rightarrow(\\\\neg p))\\\\\\\\\\n(p\\\\land(p\\\\rightarrow q)) logseq____&amp;\\\\rightarrow q logseq____&amp;\\\\quad \\\\text{Tantologie}\\n\\\\end{align}logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Flogseq____&quot;,195,536870925]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Vlogseq____&quot;,195,536870925]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ulogseq____&quot;,39,536870925]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ulogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-12ab-4f98-a349-4d9f297b19delogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Flogseq____&quot;,212,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Vlogseq____&quot;,212,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,172,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,175,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,176,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,183,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,186,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,190,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Hlogseq____&quot;,175,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Hlogseq____&quot;,176,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Hlogseq____&quot;,183,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Hlogseq____&quot;,190,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-3255-4859-8488-e35337db3ab6logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Flogseq____&quot;,201,536870925]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Vlogseq____&quot;,201,536870925]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ulogseq____&quot;,46,536870925]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ulogseq____&quot;,185,536870925]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ulogseq____&quot;,186,536870925]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ulogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Hlogseq____&quot;,46,536870925]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Hlogseq____&quot;,185,536870925]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-8580-403a-8191-b214333567a8logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussagenlogische Variable]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Flogseq____&quot;,213,536870925]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Vlogseq____&quot;,217,536870925]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,173,536870925]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870925]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Jlogseq____&quot;,[],536870925]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Hlogseq____&quot;,173,536870925]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-d545-44e8-9c4c-38d22028e4fdlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $w$ istlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Flogseq____&quot;,200,536870925]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Vlogseq____&quot;,200,536870925]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,178,536870925]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-c179-40c7-8884-41aab6e7af98logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Flogseq____&quot;,196,536870925]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Vlogseq____&quot;,217,536870925]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,172,536870925]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,186,536870925]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870925]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Jlogseq____&quot;,[],536870925]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Hlogseq____&quot;,172,536870925]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Hlogseq____&quot;,186,536870925]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-1e28-415b-ac73-6c42d9890faclogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Soweit die \\logseq____&quot;[[Syntax]]\\logseq____&quot;, jetzt die [[Semantik]]. Die [Wahrheitswerte]([[Wahrheitswert]])\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Flogseq____&quot;,198,536870925]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Vlogseq____&quot;,217,536870925]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ulogseq____&quot;,176,536870925]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ulogseq____&quot;,181,536870925]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ulogseq____&quot;,183,536870925]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ulogseq____&quot;,187,536870925]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ulogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Hlogseq____&quot;,176,536870925]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Hlogseq____&quot;,181,536870925]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Hlogseq____&quot;,183,536870925]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Hlogseq____&quot;,187,536870925]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-0ece-4f7a-b845-371c5657a7f4logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 1. [[Aussagen]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Flogseq____&quot;,199,536870925]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Vlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870925]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Jlogseq____&quot;,[],536870925]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Hlogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-bd0d-4062-8bf8-3201262f633blogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Zuordnung von $w/f$ an jede [Variable]([[Variablen]]) einer [[Aussageformel]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Flogseq____&quot;,196,536870925]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Vlogseq____&quot;,196,536870925]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ulogseq____&quot;,180,536870925]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ulogseq____&quot;,186,536870925]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ulogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ulogseq____&quot;,190,536870925]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Hlogseq____&quot;,180,536870925]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Hlogseq____&quot;,186,536870925]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-977a-4881-a242-07394bbf65fblogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Satz, der wahr oder falsch ist, d.h. der [[Wahrheitswert]] $w$ bzw $f$ hat ($t/f$, $1/0$, $\\\\text{wahr}/\\\\text{falsch}$)logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Flogseq____&quot;,214,536870925]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Vlogseq____&quot;,214,536870925]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ulogseq____&quot;,176,536870925]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Hlogseq____&quot;,176,536870925]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-928f-4ef0-9d7c-2fb65c4bc216logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Verknüpfung von Aussagen]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Flogseq____&quot;,192,536870925]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Xlogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Vlogseq____&quot;,214,536870925]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Ulogseq____&quot;,169,536870925]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Ulogseq____&quot;,184,536870925]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Ulogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870925]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Jlogseq____&quot;,[],536870925]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Hlogseq____&quot;,188,536870925]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-1f0e-4f34-aff0-2fa0c0ba321elogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sind $p$ und $q$ [[Aussagen]], so auch\\n\\\\begin{align}\\n(p\\\\land q) logseq____&amp;\\\\quadlogseq____&amp; (\\logseq____&quot;\\\\text{und}\\logseq____&quot;)\\\\\\\\\\n(p\\\\lor q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{oder}\\logseq____&quot;)\\\\\\\\\\n(\\\\neg p) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{nicht}\\logseq____&quot;)\\\\\\\\\\n(p\\\\rightarrow q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{impliziert}\\logseq____&quot;)\\\\\\\\\\n(p\\\\leftrightarrow q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{genau dann 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(Logik)logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Blogseq____&quot;,1697635828378,536870926]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-e5a8-4272-b81a-a439654500fblogseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Klogseq____&quot;,1697635828382,536870926]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^@logseq____&quot;,false,536870926]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;sprachenlogseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^11logseq____&quot;,logseq____&quot;Sprachenlogseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Blogseq____&quot;,1697635828382,536870926]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-6ec3-4c6f-950d-18fee0bbea09logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Klogseq____&quot;,1697635828379,536870926]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^@logseq____&quot;,false,536870926]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;objekt (logik)logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^11logseq____&quot;,logseq____&quot;Objekt (Logik)logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Blogseq____&quot;,1697635828379,536870926]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-b07d-49bc-8760-d57eeabd12e0logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\forall x:p(x)$ ist die [Aussage]([[Aussagen]]): $\\logseq____&quot;\\\\text{Für alle x aus U ist p(x) wahr}\\logseq____&quot;\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w\\\\quadlogseq____&amp;\\\\text{fallls p(x) w für alle x aus U}\\\\\\\\f\\\\quadlogseq____&amp;\\\\text{falls p(x) f für (wenigstens) ein x aus U}\\\\end{cases}$logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Flogseq____&quot;,256,536870926]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Vlogseq____&quot;,256,536870926]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,176,536870926]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,184,536870926]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Hlogseq____&quot;,176,536870926]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Hlogseq____&quot;,184,536870926]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-5fe8-4c09-ba7e-b22fb52fa49blogseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $x$ aus $\\\\Reals$ beliebig. Setze $y:=x+1$ (ist aus $\\\\Reals$). Dann ist $xlogseq____&lt;x+1=y$ also $xlogseq____&lt;y$. $\\\\blacksquare$logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Flogseq____&quot;,270,536870926]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Vlogseq____&quot;,270,536870926]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,39,536870926]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,228,536870926]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,231,536870926]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,232,536870926]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-0879-45df-a607-fd6673184886logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Verschiedene [[Quantoren]] dürfen **nicht** vertauscht werdenlogseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Flogseq____&quot;,278,536870926]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Vlogseq____&quot;,260,536870926]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,228,536870926]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,232,536870926]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Hlogseq____&quot;,232,536870926]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-93f7-45de-a875-726d0c79edc0logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\logseq____&quot;\\\\text{x ist prim}\\logseq____&quot; \\\\quad logseq____&amp; \\\\text{ist AF mit Variablen x über den  natürlichen Zahlen}\\\\\\\\\\n\\logseq____&quot;\\\\underbrace{x}_{x_1}logseq____&lt;\\\\underbrace{y}_{x_2}\\logseq____&quot;\\\\quad logseq____&amp;\\\\text{ist AF mit Variablen }x,y\\\\text{ über die reellen Zahlen } \\\\underbrace{\\\\Reals}_{U_1},\\\\underbrace{\\\\Reals}_{U_2}\\\\\\\\\\n\\logseq____&quot;\\\\text{x ist wahr}\\logseq____&quot;\\\\quadlogseq____&amp;\\\\text{ist AF mit Variablen x über dem Universum der Aussagen}\\n\\\\end{align}logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Flogseq____&quot;,274,536870926]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Vlogseq____&quot;,280,536870926]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-a80a-4348-818f-c3d6c9be4d79logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\exists x:p(x)$ ist die Aussage: \\logseq____&quot;Es gibt (wenigstens) ein x aus U für das $p(x)$ wahr ist\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w \\\\quadlogseq____&amp;\\\\text{falls }p(x)\\\\text{ w ist für (wenigstens) ein x aus U}\\\\\\\\f\\\\quad logseq____&amp;\\\\text{falls }p(x)\\\\text{ f ist für alle x aus U}\\\\end{cases}$logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Flogseq____&quot;,273,536870926]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Vlogseq____&quot;,280,536870926]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,176,536870926]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Hlogseq____&quot;,176,536870926]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-e595-4a74-ac57-e26ec9f26ea0logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Aussageform]] (AF) über [Universen]([[Universen (Logik)]]) $U_1,\\\\cdots,U_n$:logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Flogseq____&quot;,280,536870926]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Vlogseq____&quot;,280,536870926]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,242,536870926]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Hlogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Hlogseq____&quot;,242,536870926]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-3bfb-42d5-b0b1-177b51947fc1logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x,y)$ AF in Variablen $x,y$ über $U_1,U_2$\\n\\\\begin{align}\\n\\\\underbrace{\\\\forall x: \\\\underbrace{\\\\exists y: p(x,y)}_{\\\\text{AF in den Variablen }x\\\\text{ über }U_1}}_{\\\\text{Aussage}}\\n\\\\end{align}logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Flogseq____&quot;,253,536870926]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Vlogseq____&quot;,253,536870926]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,39,536870926]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,220,536870926]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-e44e-4bd9-9d41-0b2c6ffbb834logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Satz]] mit [[Variablen]] $x_1,\\\\cdots,x_n$, der bei Ersetzung jedes $x_j$ durch ein [Objekt]([[Objekt (Logik)]]) aus $U_j$ stets zu einer [Aussage]([[Aussagen]]) wirdlogseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Flogseq____&quot;,250,536870926]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Vlogseq____&quot;,280,536870926]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,180,536870926]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,184,536870926]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,241,536870926]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,244,536870926]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Hlogseq____&quot;,180,536870926]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Hlogseq____&quot;,184,536870926]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Hlogseq____&quot;,241,536870926]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Hlogseq____&quot;,244,536870926]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-6e3a-494b-814f-86923990fa9alogseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Schachtelung von quantoren ([Beispiel]([[Beispiele]])):logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Flogseq____&quot;,266,536870926]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Vlogseq____&quot;,272,536870926]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,39,536870926]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,220,536870926]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Hlogseq____&quot;,39,536870926]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-c556-4719-bacb-4fe8aeaa3192logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\blacksquare$ = Beweisende, auch [q.e.d.]([[Q.E.D.]]), [[w.z.b.w.]], QED, ![image.png](../assets/image_1697192491775_0.png)logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Flogseq____&quot;,246,536870926]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Vlogseq____&quot;,246,536870926]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,39,536870926]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,222,536870926]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,225,536870926]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,228,536870926]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,231,536870926]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,232,536870926]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Hlogseq____&quot;,222,536870926]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Hlogseq____&quot;,225,536870926]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-3898-44c3-bcd3-b22f95764647logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche Regeln]]logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Flogseq____&quot;,265,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Vlogseq____&quot;,265,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,221,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,226,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,229,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,230,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,236,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,237,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Hlogseq____&quot;,221,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Hlogseq____&quot;,226,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Hlogseq____&quot;,229,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Hlogseq____&quot;,230,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Hlogseq____&quot;,236,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Hlogseq____&quot;,237,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-684c-405a-93fa-2aeb9b632562logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x)$ AF in der Variablen $x$ über $U$:logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Flogseq____&quot;,248,536870926]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Vlogseq____&quot;,280,536870926]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-d0fa-4fd5-9e45-3e85457e99felogseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Flogseq____&quot;,269,536870926]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Vlogseq____&quot;,280,536870926]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,39,536870926]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Hlogseq____&quot;,39,536870926]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-0ff3-408c-b2a2-3f0f6d99c876logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nlogseq____&amp;\\\\neg\\\\left(\\\\forall x :\\\\exists y :\\\\forall w :\\\\forall u :\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)\\\\right)\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x:(\\\\neg(\\\\exists y: \\\\forall w: \\\\forall u: \\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x:\\\\forall y:(\\\\neg(\\\\forall w: \\\\forall u:\\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x:\\\\forall y:\\\\exists w:(\\\\neg(\\\\forall u:\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x: \\\\forall y: \\\\exists w: \\\\exists u : \\\\forall z:\\\\neg(p(x,y,z)\\\\rightarrow q(u,w))\\n\\\\end{align}logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Flogseq____&quot;,257,536870926]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Vlogseq____&quot;,257,536870926]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,39,536870926]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-3978-49ac-84d7-bdc825991dadlogseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Regeln]]logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Flogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Vlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,220,536870926]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870926]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Jlogseq____&quot;,[],536870926]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Hlogseq____&quot;,220,536870926]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^17logseq____&quot;,false,536870926]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-1553-4060-8015-e309f5aa7a3blogseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nlogseq____&amp;\\\\forall x: \\\\forall y: p(x, y) \\\\equiv \\\\forall y: \\\\forall x: p(x,y)\\\\\\\\\\nlogseq____&amp;\\\\exists x:\\\\exists y:p(x,y)\\\\equiv\\\\exists y:\\\\exists x:p(x,y)\\\\\\\\\\nlogseq____&amp;[\\\\forall x_1:\\\\forall x_2: \\\\cdots:\\\\forall x_n:p(x_1,x_2,\\\\cdots,x_n)\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\equiv\\\\forall_{x_{\\\\pi(1)}}:\\\\forall_{x_{\\\\pi(1)}}:\\\\cdots:\\\\forall_{x_{\\\\pi(1)}}:p(x_1,x_2,\\\\cdots,x_n)\\n\\\\end{align}logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Flogseq____&quot;,269,536870926]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Vlogseq____&quot;,269,536870926]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,228,536870926]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,232,536870926]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-9a48-4983-8427-0a5866c1035blogseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Widerspruch = ↯, #logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Flogseq____&quot;,276,536870926]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Vlogseq____&quot;,276,536870926]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,39,536870926]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,228,536870926]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,231,536870926]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,232,536870926]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-a16f-4a94-866d-d0c0a7e2f262logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Allquantor]] [[Existenzquantor]]logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Flogseq____&quot;,273,536870926]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Vlogseq____&quot;,273,536870926]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,233,536870926]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,239,536870926]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Hlogseq____&quot;,233,536870926]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Hlogseq____&quot;,239,536870926]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-c5e7-4ee6-a955-fe39225b7463logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXMElogseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Flogseq____&quot;,281,536870926]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Vlogseq____&quot;,281,536870926]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,46,536870926]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Hlogseq____&quot;,46,536870926]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-b76b-4afc-bc69-64898f53786blogseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Betrachte $\\logseq____&quot;xlogseq____&lt;y\\logseq____&quot;$ als AF über $\\\\Reals, \\\\Reals$logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Flogseq____&quot;,267,536870926]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Vlogseq____&quot;,267,536870926]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,39,536870926]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,228,536870926]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,232,536870926]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-0690-4d10-8c1a-b8d733daeb26logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n(p\\\\land q)\\\\land r logseq____&amp;\\\\equiv p\\\\land(q\\\\land r),\\\\quadlogseq____&amp;\\\\text{schreibe daher: }  p\\\\land q\\\\land r,\\\\quad \\\\land \\\\text{ assoziativ}\\\\\\\\\\n(p \\\\lor q) \\\\lor r logseq____&amp;\\\\equiv p \\\\lor (q\\\\lor r),\\\\quadlogseq____&amp;\\\\text{schreibe daher: } p\\\\lor q\\\\lor r,\\\\quad \\\\lor \\\\text{ assoziativ}\\\\\\\\\\np \\\\land q logseq____&amp;\\\\equiv q \\\\land p,\\\\quad \\\\land logseq____&amp;\\\\text{ kommutativ}\\\\\\\\\\np \\\\lor q logseq____&amp;\\\\equiv q \\\\lor p,\\\\quad \\\\lor logseq____&amp;\\\\text{ kommutativ}\\\\\\\\\\n\\\\neg(\\\\neg p) logseq____&amp;\\\\equiv p, \\\\quad \\\\neg logseq____&amp;\\\\text{ idenpotent}\\\\\\\\\\np\\\\land(q\\\\lor r)logseq____&amp;\\\\equiv (p\\\\land q)\\\\lor(p\\\\land r);\\\\notag\\\\\\\\\\np\\\\lor(q\\\\land r)logseq____&amp;\\\\equiv (p\\\\lor q)\\\\lor(p\\\\land r),\\\\quad logseq____&amp;\\\\land,\\\\lor\\\\text{ wechselseitig distributiv}\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&amp;\\\\equiv(\\\\neg p)\\\\lor(\\\\neg q);\\\\notag\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&amp;\\\\equiv(\\\\neg p)\\\\land (\\\\neg q), \\\\quad logseq____&amp;\\\\text{ (kleine) de Morgansche Regeln}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Flogseq____&quot;,259,536870926]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Vlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-2c7b-46ec-bf79-aea144e40069logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:(p(x)\\\\land q(x)) logseq____&amp;\\\\equiv (\\\\forall x: p(x)) \\\\land (\\\\forall x:q(x));\\\\notag\\\\\\\\\\n\\\\exists x: (p(x) \\\\lor q(x)) logseq____&amp;\\\\equiv (\\\\exists x: p(x))\\\\lor(\\\\exists x: q(x)),\\\\quadlogseq____&amp;\\\\text{Große Assoziativgesetze}\\\\\\\\\\n\\\\neg(\\\\forall x:p(x))logseq____&amp;\\\\equiv \\\\exists x: (\\\\neg p(x));\\\\quadlogseq____&amp;\\\\text{Große de Morgansche Regeln;}\\\\notag\\\\\\\\\\n\\\\neg(\\\\exists x: p(x)) logseq____&amp;\\\\equiv \\\\forall x: (\\\\neg p(x)),\\\\quadlogseq____&amp;\\\\text{Negationsregeln.}\\n\\\\end{align}logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Flogseq____&quot;,272,536870926]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Vlogseq____&quot;,272,536870926]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,220,536870926]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-ae0d-421a-bb88-5627ddabbe20logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Flogseq____&quot;,260,536870926]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Vlogseq____&quot;,269,536870926]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,39,536870926]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,228,536870926]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,232,536870926]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Hlogseq____&quot;,39,536870926]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-e53f-43ed-85e1-ca12509439a6logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Die beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der [[Aussagenlogik]]logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Flogseq____&quot;,256,536870926]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Vlogseq____&quot;,280,536870926]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,224,536870926]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,243,536870926]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Hlogseq____&quot;,224,536870926]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Hlogseq____&quot;,243,536870926]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-7ce7-431f-9588-99cdc604bd90logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Gleichartige]([[Gleichartig]]) [[Quantoren]] dürfen vertauscht werdenlogseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Flogseq____&quot;,272,536870926]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Vlogseq____&quot;,280,536870926]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,228,536870926]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,232,536870926]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Hlogseq____&quot;,228,536870926]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Hlogseq____&quot;,232,536870926]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-b084-4cdb-8b1c-5958e845abeflogseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist wahr}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Flogseq____&quot;,264,536870926]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Vlogseq____&quot;,264,536870926]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,39,536870926]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,228,536870926]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,231,536870926]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,232,536870926]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Hlogseq____&quot;,231,536870926]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-7a78-419d-bca9-0a9b4ca57ad8logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Für das leere Universum gilt\\n\\\\begin{align}\\n\\\\forall x: p(x)\\\\quadlogseq____&amp;Tautologie\\\\\\\\\\n\\\\exists x: p(x)\\\\quadlogseq____&amp;Kontradiktion\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Flogseq____&quot;,268,536870926]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Vlogseq____&quot;,280,536870926]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-c5b1-43f5-a161-5884d61dff65logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Regeln]]logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Flogseq____&quot;,281,536870926]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Vlogseq____&quot;,280,536870926]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Ulogseq____&quot;,220,536870926]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870926]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Jlogseq____&quot;,[],536870926]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Hlogseq____&quot;,220,536870926]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-6728-4ca7-8876-028bf9f4a9a8logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\underbrace{\\\\forall}_\\\\text{Allquantor} x: p(x) logseq____&amp;\\\\equiv p(O_1) \\\\land p(O_2) \\\\land \\\\cdots \\\\land p(O_m)\\\\\\\\\\n\\\\underbrace{\\\\exists}_\\\\text{Existenzquantor} x: p(x) logseq____&amp;\\\\equiv p(0_1) \\\\lor p(O_2) \\\\lor \\\\cdots \\\\lor p(0_m)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Flogseq____&quot;,282,536870926]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Vlogseq____&quot;,280,536870926]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-03c8-40cb-b626-c3262d70c8d3logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^Flogseq____&quot;,252,536870926]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^Vlogseq____&quot;,280,536870926]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^Ulogseq____&quot;,39,536870926]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^Hlogseq____&quot;,39,536870926]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-a095-4719-a043-0dfe8e23a367logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[275,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Nach Ersetzung von $x$ in der AF $\\logseq____&quot;xlogseq____&lt;y\\logseq____&quot;$ durch eine konkrete Zahl entsteht eine AF in der Variablen $y$, z. Bsp. $\\logseq____&quot;17logseq____&lt;y\\logseq____&quot;$logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[275,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[275,logseq____&quot;^Flogseq____&quot;,248,536870926]],[logseq____&quot;^15logseq____&quot;,[275,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[275,logseq____&quot;^Vlogseq____&quot;,248,536870926]],[logseq____&quot;^15logseq____&quot;,[275,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[275,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[275,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[275,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-0a6a-48b6-ab5e-adad12a58bfflogseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Wäre $y$ aus $\\\\Reals$ mit $xlogseq____&lt;y$ für alle $x$ aus $\\\\Reals$, so insbesondere auch $ylogseq____&lt;y$, Widerspruch. $\\\\blacksquare$logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^Flogseq____&quot;,279,536870926]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^Xlogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^Vlogseq____&quot;,279,536870926]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^Ulogseq____&quot;,39,536870926]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^Ulogseq____&quot;,227,536870926]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^Ulogseq____&quot;,228,536870926]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^Ulogseq____&quot;,231,536870926]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^Ulogseq____&quot;,232,536870926]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^Ulogseq____&quot;,238,536870926]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^17logseq____&quot;,true,536870926]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-586a-4b73-bb22-f2e752942185logseq____&quot;,536870926]],[logseq____&quot;^15logseq____&quot;,[277,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] 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} x=\\\\frac25 \\\\text{ und } y=\\\\frac37 \\\\text{ ist }\\\\frac xy$\\n\\\\begin{align}\\n\\\\frac xy = \\\\frac{\\\\frac25}{\\\\frac37} = 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[[Logarithmen]]logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[343,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[343,logseq____&quot;^Flogseq____&quot;,338,536870936]],[logseq____&quot;^15logseq____&quot;,[343,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[343,logseq____&quot;^Vlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[343,logseq____&quot;^Ulogseq____&quot;,35,536870936]],[logseq____&quot;^15logseq____&quot;,[343,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[343,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870936]],[logseq____&quot;^15logseq____&quot;,[343,logseq____&quot;^Jlogseq____&quot;,[],536870936]],[logseq____&quot;^15logseq____&quot;,[343,logseq____&quot;^Hlogseq____&quot;,35,536870936]],[logseq____&quot;^15logseq____&quot;,[343,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[343,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-537e-44c5-baa4-21d5e10288e6logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[344,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[344,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[344,logseq____&quot;^Flogseq____&quot;,365,536870936]],[logseq____&quot;^15logseq____&quot;,[344,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[344,logseq____&quot;^Vlogseq____&quot;,365,536870936]],[logseq____&quot;^15logseq____&quot;,[344,logseq____&quot;^Ulogseq____&quot;,32,536870936]],[logseq____&quot;^15logseq____&quot;,[344,logseq____&quot;^Ulogseq____&quot;,36,536870936]],[logseq____&quot;^15logseq____&quot;,[344,logseq____&quot;^Ulogseq____&quot;,38,536870936]],[logseq____&quot;^15logseq____&quot;,[344,logseq____&quot;^Ulogseq____&quot;,42,536870936]],[logseq____&quot;^15logseq____&quot;,[344,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[344,logseq____&quot;^Hlogseq____&quot;,42,536870936]],[logseq____&quot;^15logseq____&quot;,[344,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[344,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-d53e-41bc-9da8-88f9c95943ealogseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[345,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\na^nlogseq____&amp;=\\\\underbrace{a*a*\\\\cdots*n}_n logseq____&amp; a,blogseq____&gt;0\\\\\\\\\\na^2b^2logseq____&amp;=(ab)^n\\\\\\\\\\n\\\\frac{a^n}{b^n}logseq____&amp;=\\\\left(\\\\frac ab\\\\right)^n\\\\\\\\\\na^na^mlogseq____&amp;=a^{n+m}\\\\\\\\\\n\\\\frac1{a^n}logseq____&amp;=a^{-n}\\\\\\\\\\n(a^n)^mlogseq____&amp;=a^{nm}\\\\\\\\\\na^0logseq____&amp;=1\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[345,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[345,logseq____&quot;^Flogseq____&quot;,376,536870936]],[logseq____&quot;^15logseq____&quot;,[345,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[345,logseq____&quot;^Vlogseq____&quot;,376,536870936]],[logseq____&quot;^15logseq____&quot;,[345,logseq____&quot;^Ulogseq____&quot;,31,536870936]],[logseq____&quot;^15logseq____&quot;,[345,logseq____&quot;^Ulogseq____&quot;,41,536870936]],[logseq____&quot;^15logseq____&quot;,[345,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[345,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[345,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-10b3-4086-832b-795642284854logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[346,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[346,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[346,logseq____&quot;^Flogseq____&quot;,387,536870936]],[logseq____&quot;^15logseq____&quot;,[346,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[346,logseq____&quot;^Vlogseq____&quot;,373,536870936]],[logseq____&quot;^15logseq____&quot;,[346,logseq____&quot;^Ulogseq____&quot;,32,536870936]],[logseq____&quot;^15logseq____&quot;,[346,logseq____&quot;^Ulogseq____&quot;,38,536870936]],[logseq____&quot;^15logseq____&quot;,[346,logseq____&quot;^Ulogseq____&quot;,39,536870936]],[logseq____&quot;^15logseq____&quot;,[346,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[346,logseq____&quot;^Ulogseq____&quot;,46,536870936]],[logseq____&quot;^15logseq____&quot;,[346,logseq____&quot;^Hlogseq____&quot;,46,536870936]],[logseq____&quot;^15logseq____&quot;,[346,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[346,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-c604-4f7a-a5ef-3440faaf83a6logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[347,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Rationalmachen]] des [[Nenner]]slogseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[347,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[347,logseq____&quot;^Flogseq____&quot;,389,536870936]],[logseq____&quot;^15logseq____&quot;,[347,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[347,logseq____&quot;^Vlogseq____&quot;,349,536870936]],[logseq____&quot;^15logseq____&quot;,[347,logseq____&quot;^Ulogseq____&quot;,31,536870936]],[logseq____&quot;^15logseq____&quot;,[347,logseq____&quot;^Ulogseq____&quot;,41,536870936]],[logseq____&quot;^15logseq____&quot;,[347,logseq____&quot;^Ulogseq____&quot;,43,536870936]],[logseq____&quot;^15logseq____&quot;,[347,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[347,logseq____&quot;^Ulogseq____&quot;,49,536870936]],[logseq____&quot;^15logseq____&quot;,[347,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870936]],[logseq____&quot;^15logseq____&quot;,[347,logseq____&quot;^Jlogseq____&quot;,[],536870936]],[logseq____&quot;^15logseq____&quot;,[347,logseq____&quot;^Hlogseq____&quot;,43,536870936]],[logseq____&quot;^15logseq____&quot;,[347,logseq____&quot;^Hlogseq____&quot;,49,536870936]],[logseq____&quot;^15logseq____&quot;,[347,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[347,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-accd-4551-89e5-a55f198294d3logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[348,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____&gt;0$ welche keinen Sinn ergibtlogseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[348,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[348,logseq____&quot;^Flogseq____&quot;,357,536870936]],[logseq____&quot;^15logseq____&quot;,[348,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[348,logseq____&quot;^Vlogseq____&quot;,350,536870936]],[logseq____&quot;^15logseq____&quot;,[348,logseq____&quot;^Ulogseq____&quot;,31,536870936]],[logseq____&quot;^15logseq____&quot;,[348,logseq____&quot;^Ulogseq____&quot;,39,536870936]],[logseq____&quot;^15logseq____&quot;,[348,logseq____&quot;^Ulogseq____&quot;,41,536870936]],[logseq____&quot;^15logseq____&quot;,[348,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[348,logseq____&quot;^Ulogseq____&quot;,46,536870936]],[logseq____&quot;^15logseq____&quot;,[348,logseq____&quot;^Hlogseq____&quot;,46,536870936]],[logseq____&quot;^15logseq____&quot;,[348,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[348,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-7fa8-4614-bd97-ca55848ffe90logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[349,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Wurzeln]]logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[349,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[349,logseq____&quot;^Flogseq____&quot;,376,536870936]],[logseq____&quot;^15logseq____&quot;,[349,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[349,logseq____&quot;^Vlogseq____&quot;,354,536870936]],[logseq____&quot;^15logseq____&quot;,[349,logseq____&quot;^Ulogseq____&quot;,31,536870936]],[logseq____&quot;^15logseq____&quot;,[349,logseq____&quot;^Ulogseq____&quot;,41,536870936]],[logseq____&quot;^15logseq____&quot;,[349,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[349,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870936]],[logseq____&quot;^15logseq____&quot;,[349,logseq____&quot;^Jlogseq____&quot;,[],536870936]],[logseq____&quot;^15logseq____&quot;,[349,logseq____&quot;^Hlogseq____&quot;,41,536870936]],[logseq____&quot;^15logseq____&quot;,[349,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[349,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-7aca-48aa-830b-5abaae42cf88logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[350,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[350,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[350,logseq____&quot;^Flogseq____&quot;,370,536870936]],[logseq____&quot;^15logseq____&quot;,[350,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[350,logseq____&quot;^Vlogseq____&quot;,349,536870936]],[logseq____&quot;^15logseq____&quot;,[350,logseq____&quot;^Ulogseq____&quot;,31,536870936]],[logseq____&quot;^15logseq____&quot;,[350,logseq____&quot;^Ulogseq____&quot;,39,536870936]],[logseq____&quot;^15logseq____&quot;,[350,logseq____&quot;^Ulogseq____&quot;,41,536870936]],[logseq____&quot;^15logseq____&quot;,[350,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[350,logseq____&quot;^Hlogseq____&quot;,39,536870936]],[logseq____&quot;^15logseq____&quot;,[350,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[350,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-4885-4a35-a92c-13fcf11bd9a5logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[351,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[351,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[351,logseq____&quot;^Flogseq____&quot;,383,536870936]],[logseq____&quot;^15logseq____&quot;,[351,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[351,logseq____&quot;^Vlogseq____&quot;,383,536870936]],[logseq____&quot;^15logseq____&quot;,[351,logseq____&quot;^Ulogseq____&quot;,40,536870936]],[logseq____&quot;^15logseq____&quot;,[351,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[351,logseq____&quot;^Ulogseq____&quot;,46,536870936]],[logseq____&quot;^15logseq____&quot;,[351,logseq____&quot;^Hlogseq____&quot;,46,536870936]],[logseq____&quot;^15logseq____&quot;,[351,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[351,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-1f12-45f6-a818-b0b7a1d3cb2blogseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[352,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[352,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[352,logseq____&quot;^Flogseq____&quot;,337,536870936]],[logseq____&quot;^15logseq____&quot;,[352,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[352,logseq____&quot;^Vlogseq____&quot;,347,536870936]],[logseq____&quot;^15logseq____&quot;,[352,logseq____&quot;^Ulogseq____&quot;,31,536870936]],[logseq____&quot;^15logseq____&quot;,[352,logseq____&quot;^Ulogseq____&quot;,39,536870936]],[logseq____&quot;^15logseq____&quot;,[352,logseq____&quot;^Ulogseq____&quot;,41,536870936]],[logseq____&quot;^15logseq____&quot;,[352,logseq____&quot;^Ulogseq____&quot;,43,536870936]],[logseq____&quot;^15logseq____&quot;,[352,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[352,logseq____&quot;^Ulogseq____&quot;,49,536870936]],[logseq____&quot;^15logseq____&quot;,[352,logseq____&quot;^Hlogseq____&quot;,39,536870936]],[logseq____&quot;^15logseq____&quot;,[352,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[352,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-3ff7-4bec-a470-4cdb117f99cflogseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[353,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Quadratische Gleichungen]]logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[353,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[353,logseq____&quot;^Flogseq____&quot;,349,536870936]],[logseq____&quot;^15logseq____&quot;,[353,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[353,logseq____&quot;^Vlogseq____&quot;,354,536870936]],[logseq____&quot;^15logseq____&quot;,[353,logseq____&quot;^Ulogseq____&quot;,31,536870936]],[logseq____&quot;^15logseq____&quot;,[353,logseq____&quot;^Ulogseq____&quot;,33,536870936]],[logseq____&quot;^15logseq____&quot;,[353,logseq____&quot;^Ulogseq____&quot;,41,536870936]],[logseq____&quot;^15logseq____&quot;,[353,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[353,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870936]],[logseq____&quot;^15logseq____&quot;,[353,logseq____&quot;^Jlogseq____&quot;,[],536870936]],[logseq____&quot;^15logseq____&quot;,[353,logseq____&quot;^Hlogseq____&quot;,33,536870936]],[logseq____&quot;^15logseq____&quot;,[353,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[353,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-16b5-4e78-a6c7-6fd2871af755logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[354,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Potenzen]] und [[Wurzeln]]logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[354,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[354,logseq____&quot;^Flogseq____&quot;,381,536870936]],[logseq____&quot;^15logseq____&quot;,[354,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[354,logseq____&quot;^Vlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[354,logseq____&quot;^Ulogseq____&quot;,31,536870936]],[logseq____&quot;^15logseq____&quot;,[354,logseq____&quot;^Ulogseq____&quot;,41,536870936]],[logseq____&quot;^15logseq____&quot;,[354,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[354,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870936]],[logseq____&quot;^15logseq____&quot;,[354,logseq____&quot;^Jlogseq____&quot;,[],536870936]],[logseq____&quot;^15logseq____&quot;,[354,logseq____&quot;^Hlogseq____&quot;,31,536870936]],[logseq____&quot;^15logseq____&quot;,[354,logseq____&quot;^Hlogseq____&quot;,41,536870936]],[logseq____&quot;^15logseq____&quot;,[354,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[354,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-06f2-4b16-9e99-a81d08f5ae48logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[355,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Allgemein}$\\n\\\\begin{align}\\n(a+b)^2logseq____&amp;=a^2+2ab+b^2logseq____&amp;,\\\\text{ 1. Binomische Formel}\\\\\\\\\\n(a-b)^2logseq____&amp;=a^2-2ab+b^2logseq____&amp;,\\\\text{ 2. Binomische Formel}\\\\\\\\\\n(a+b)(a-b)logseq____&amp;=a^2-b^2logseq____&amp;,\\\\text{ 3. Binomische 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\\\\cdots\\\\end{array}logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[368,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[368,logseq____&quot;^Flogseq____&quot;,366,536870936]],[logseq____&quot;^15logseq____&quot;,[368,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[368,logseq____&quot;^Vlogseq____&quot;,366,536870936]],[logseq____&quot;^15logseq____&quot;,[368,logseq____&quot;^Ulogseq____&quot;,32,536870936]],[logseq____&quot;^15logseq____&quot;,[368,logseq____&quot;^Ulogseq____&quot;,38,536870936]],[logseq____&quot;^15logseq____&quot;,[368,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[368,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[368,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-eeb7-4f5a-80be-28e5c015e215logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[369,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])\\n\\\\begin{align}\\nx^4-34x^2+225logseq____&amp;=0\\\\\\\\\\n\\\\text{substituiert 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[[Potenzen]]logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[376,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[376,logseq____&quot;^Flogseq____&quot;,354,536870936]],[logseq____&quot;^15logseq____&quot;,[376,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[376,logseq____&quot;^Vlogseq____&quot;,354,536870936]],[logseq____&quot;^15logseq____&quot;,[376,logseq____&quot;^Ulogseq____&quot;,31,536870936]],[logseq____&quot;^15logseq____&quot;,[376,logseq____&quot;^Ulogseq____&quot;,41,536870936]],[logseq____&quot;^15logseq____&quot;,[376,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[376,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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x=-\\\\frac{11}{12}\\n\\\\end{align}logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[378,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[378,logseq____&quot;^Flogseq____&quot;,334,536870936]],[logseq____&quot;^15logseq____&quot;,[378,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[378,logseq____&quot;^Vlogseq____&quot;,334,536870936]],[logseq____&quot;^15logseq____&quot;,[378,logseq____&quot;^Ulogseq____&quot;,31,536870936]],[logseq____&quot;^15logseq____&quot;,[378,logseq____&quot;^Ulogseq____&quot;,34,536870936]],[logseq____&quot;^15logseq____&quot;,[378,logseq____&quot;^Ulogseq____&quot;,41,536870936]],[logseq____&quot;^15logseq____&quot;,[378,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[378,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[378,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-9c3c-4213-b231-00548bc08c76logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[379,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\frac12 \\\\sqrt2, \\\\frac12, \\\\frac12\\\\sqrt3 \\\\text{ sind werte von }\\\\sin x$\\n\\\\begin{align}\\n\\\\sin 30\\\\degreelogseq____&amp;=\\\\frac12\\\\\\\\\\n\\\\sin 45\\\\degree logseq____&amp;= \\\\frac12\\\\sqrt2 \\\\\\\\\\n\\\\sin 60\\\\degree logseq____&amp;= \\\\frac12 \\\\sqrt3 \\\\\\\\\\n\\\\end{align}logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[379,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[379,logseq____&quot;^Flogseq____&quot;,374,536870936]],[logseq____&quot;^15logseq____&quot;,[379,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[379,logseq____&quot;^Vlogseq____&quot;,374,536870936]],[logseq____&quot;^15logseq____&quot;,[379,logseq____&quot;^Ulogseq____&quot;,40,536870936]],[logseq____&quot;^15logseq____&quot;,[379,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[379,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[379,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-878c-48cd-a5b2-c24d2a406e7blogseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[380,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Herleitung mit }$[[Quadratische Ergänzung]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&amp;=0logseq____&amp;|logseq____&amp;-q\\\\\\\\\\nx^2+pxlogseq____&amp;=-qlogseq____&amp;|logseq____&amp;+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\nx^2+px+\\\\left(\\\\frac p2\\\\right)^2logseq____&amp;=-q+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\n\\\\underbrace{\\\\left(x+\\\\frac p2\\\\right)^2}_\\\\text{1. binomische Formel}logseq____&amp;=-q+\\\\left(\\\\frac p2\\\\right)^2logseq____&amp;|logseq____&amp;\\\\sqrt{()}\\\\\\\\\\n\\\\left|x+\\\\frac p2\\\\right|logseq____&amp;=\\\\sqrt{\\\\frac{p^2}4-q}logseq____&amp;,logseq____&amp;\\\\text{ falls }\\\\frac{p^2}4-q\\\\ge0\\\\\\\\\\nx+\\\\frac p2logseq____&amp;=\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}logseq____&amp;|logseq____&amp;-\\\\frac p2\\\\\\\\\\nxlogseq____&amp;=-\\\\frac p2\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[380,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[380,logseq____&quot;^Flogseq____&quot;,367,536870936]],[logseq____&quot;^15logseq____&quot;,[380,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[380,logseq____&quot;^Vlogseq____&quot;,367,536870936]],[logseq____&quot;^15logseq____&quot;,[380,logseq____&quot;^Ulogseq____&quot;,30,536870936]],[logseq____&quot;^15logseq____&quot;,[380,logseq____&quot;^Ulogseq____&quot;,31,536870936]],[logseq____&quot;^15logseq____&quot;,[380,logseq____&quot;^Ulogseq____&quot;,33,536870936]],[logseq____&quot;^15logseq____&quot;,[380,logseq____&quot;^Ulogseq____&quot;,41,536870936]],[logseq____&quot;^15logseq____&quot;,[380,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[380,logseq____&quot;^Ulogseq____&quot;,47,536870936]],[logseq____&quot;^15logseq____&quot;,[380,logseq____&quot;^Hlogseq____&quot;,30,536870936]],[logseq____&quot;^15logseq____&quot;,[380,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[380,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-8a31-42fd-bc09-c59baa97cb41logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[381,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Binomische Formeln]]logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[381,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[381,logseq____&quot;^Flogseq____&quot;,374,536870936]],[logseq____&quot;^15logseq____&quot;,[381,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[381,logseq____&quot;^Vlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[381,logseq____&quot;^Ulogseq____&quot;,38,536870936]],[logseq____&quot;^15logseq____&quot;,[381,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[381,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870936]],[logseq____&quot;^15logseq____&quot;,[381,logseq____&quot;^Jlogseq____&quot;,[],536870936]],[logseq____&quot;^15logseq____&quot;,[381,logseq____&quot;^Hlogseq____&quot;,38,536870936]],[logseq____&quot;^15logseq____&quot;,[381,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[381,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-9e31-4f85-adfc-71f8b8749f5flogseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[382,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche quadratische Gleichung hat die Lösung}$\\n$x_1=3\\\\quad x_2=4$\\n\\\\begin{align}\\nx_1+x_2 = 7 logseq____&amp;= p logseq____&amp;, x_1x_2=12=q\\\\\\\\\\nx^2+px+qlogseq____&amp;=0\\\\\\\\\\nx^2-7x+12logseq____&amp;=0\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[382,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[382,logseq____&quot;^Flogseq____&quot;,356,536870936]],[logseq____&quot;^15logseq____&quot;,[382,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[382,logseq____&quot;^Vlogseq____&quot;,356,536870936]],[logseq____&quot;^15logseq____&quot;,[382,logseq____&quot;^Ulogseq____&quot;,31,536870936]],[logseq____&quot;^15logseq____&quot;,[382,logseq____&quot;^Ulogseq____&quot;,33,536870936]],[logseq____&quot;^15logseq____&quot;,[382,logseq____&quot;^Ulogseq____&quot;,39,536870936]],[logseq____&quot;^15logseq____&quot;,[382,logseq____&quot;^Ulogseq____&quot;,41,536870936]],[logseq____&quot;^15logseq____&quot;,[382,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[382,logseq____&quot;^Ulogseq____&quot;,45,536870936]],[logseq____&quot;^15logseq____&quot;,[382,logseq____&quot;^Ulogseq____&quot;,47,536870936]],[logseq____&quot;^15logseq____&quot;,[382,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[382,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-7997-4e09-be09-b97df194a965logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[383,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\n\\\\tan x logseq____&amp;= \\\\frac{\\\\sin x}{\\\\cos x} logseq____&amp;, \\\\cos x \\\\ne 0\\\\\\\\\\n\\\\sin^{-2}x-\\\\cos^2xlogseq____&amp;=1logseq____&amp;,f\\\\\\\\\\n\\\\sin x = \\\\cos x logseq____&amp;= 1 logseq____&amp;, f\\\\\\\\\\n\\\\sin^{-2}x+cos^2ylogseq____&amp;=1logseq____&amp;,r\\\\\\\\\\n1+tan^2xlogseq____&amp;=\\\\frac1{\\\\cos^2x}logseq____&amp;,\\\\cos x\\\\ne0\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[383,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[383,logseq____&quot;^Flogseq____&quot;,379,536870936]],[logseq____&quot;^15logseq____&quot;,[383,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[383,logseq____&quot;^Vlogseq____&quot;,374,536870936]],[logseq____&quot;^15logseq____&quot;,[383,logseq____&quot;^Ulogseq____&quot;,40,536870936]],[logseq____&quot;^15logseq____&quot;,[383,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[383,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[383,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-5d60-4947-8781-9edb8c5646f5logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[384,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Die Lösung von } x^n-a=0 \\\\text{ ist } x=\\\\sqrt[n]a$ #FIXME ich glaube hier fehlt logseq____&gt;0 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Gleichungen sind richtig?}$\\n$\\\\text{Wenn } 10^x=y \\\\text{, dann}$\\n\\\\begin{align}\\nxlogseq____&amp;=\\\\lg y logseq____&amp; ,r\\\\\\\\\\nxlogseq____&amp;=\\\\log_y10logseq____&amp;,f\\\\\\\\\\nxlogseq____&amp;=\\\\log_{10}ylogseq____&amp;,r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&amp;= \\\\ln 2 logseq____&amp;, r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&amp;= \\\\ln 8 logseq____&amp;, f \\\\\\\\\\n\\\\ln 4 + \\\\ln 2 logseq____&amp;= \\\\ln 8 logseq____&amp;, r \\\\\\\\\\n\\\\end{align}logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[385,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[385,logseq____&quot;^Flogseq____&quot;,343,536870936]],[logseq____&quot;^15logseq____&quot;,[385,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[385,logseq____&quot;^Vlogseq____&quot;,343,536870936]],[logseq____&quot;^15logseq____&quot;,[385,logseq____&quot;^Ulogseq____&quot;,35,536870936]],[logseq____&quot;^15logseq____&quot;,[385,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[385,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[385,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-e291-41f7-b28d-130131cc5dd7logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[386,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Links]]logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[386,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[386,logseq____&quot;^Flogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[386,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[386,logseq____&quot;^Vlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[386,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[386,logseq____&quot;^Ulogseq____&quot;,48,536870936]],[logseq____&quot;^15logseq____&quot;,[386,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870936]],[logseq____&quot;^15logseq____&quot;,[386,logseq____&quot;^Jlogseq____&quot;,[],536870936]],[logseq____&quot;^15logseq____&quot;,[386,logseq____&quot;^Hlogseq____&quot;,48,536870936]],[logseq____&quot;^15logseq____&quot;,[386,logseq____&quot;^17logseq____&quot;,false,536870936]],[logseq____&quot;^15logseq____&quot;,[386,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-3764-4493-a57b-113d14b19196logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[387,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n(2x+y)^4logseq____&amp;=(2x)^4+4*(2x)^3y+6*(2x)^2y^2+4*2xy^3+y^4\\\\notag\\\\\\\\\\nlogseq____&amp;=16x^4+32x^3y+24x^2y^2+8xy^3+y^4\\\\\\\\\\n(1+\\\\sqrt x)^5*(1-\\\\sqrt 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logseq____&amp;\\\\text{ falls } y\\\\ge0\\\\\\\\\\n-y logseq____&amp;\\\\text{ falls } ylogseq____&lt;0\\\\\\\\\\n\\\\end{cases}\\n\\\\end{align}logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[389,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[389,logseq____&quot;^Flogseq____&quot;,350,536870936]],[logseq____&quot;^15logseq____&quot;,[389,logseq____&quot;^Xlogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[389,logseq____&quot;^Vlogseq____&quot;,349,536870936]],[logseq____&quot;^15logseq____&quot;,[389,logseq____&quot;^Ulogseq____&quot;,31,536870936]],[logseq____&quot;^15logseq____&quot;,[389,logseq____&quot;^Ulogseq____&quot;,41,536870936]],[logseq____&quot;^15logseq____&quot;,[389,logseq____&quot;^Ulogseq____&quot;,44,536870936]],[logseq____&quot;^15logseq____&quot;,[389,logseq____&quot;^17logseq____&quot;,true,536870936]],[logseq____&quot;^15logseq____&quot;,[389,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-143c-42ae-a040-67bc305c1778logseq____&quot;,536870936]],[logseq____&quot;^15logseq____&quot;,[391,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Betragsungleichungen]]logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[391,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[391,logseq____&quot;^Flogseq____&quot;,431,536870937]],[logseq____&quot;^15logseq____&quot;,[391,logseq____&quot;^Xlogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[391,logseq____&quot;^Vlogseq____&quot;,403,536870937]],[logseq____&quot;^15logseq____&quot;,[391,logseq____&quot;^Ulogseq____&quot;,117,536870937]],[logseq____&quot;^15logseq____&quot;,[391,logseq____&quot;^Ulogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[391,logseq____&quot;^Ulogseq____&quot;,119,536870937]],[logseq____&quot;^15logseq____&quot;,[391,logseq____&quot;^Ulogseq____&quot;,122,536870937]],[logseq____&quot;^15logseq____&quot;,[391,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870937]],[logseq____&quot;^15logseq____&quot;,[391,logseq____&quot;^Jlogseq____&quot;,[],536870937]],[logseq____&quot;^15logseq____&quot;,[391,logseq____&quot;^Hlogseq____&quot;,119,536870937]],[logseq____&quot;^15logseq____&quot;,[391,logseq____&quot;^17logseq____&quot;,true,536870937]],[logseq____&quot;^15logseq____&quot;,[391,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-8f3f-4282-9fd3-a55e2ae24abclogseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[392,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 1}\\\\quad xlogseq____&lt;3$\\n\\\\begin{align}\\n|x-3|logseq____&amp;=-x+3\\\\\\\\\\n-x+3logseq____&amp;logseq____&lt;5 logseq____&amp;|logseq____&amp;-3\\\\\\\\\\n-xlogseq____&amp;logseq____&lt;2 logseq____&amp;|logseq____&amp;*-1\\\\\\\\\\nxlogseq____&amp;logseq____&gt;-2\\\\\\\\\\nL_1logseq____&amp;=(-2,3)\\n\\\\end{align}logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[392,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[392,logseq____&quot;^Flogseq____&quot;,414,536870937]],[logseq____&quot;^15logseq____&quot;,[392,logseq____&quot;^Xlogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[392,logseq____&quot;^Vlogseq____&quot;,414,536870937]],[logseq____&quot;^15logseq____&quot;,[392,logseq____&quot;^Ulogseq____&quot;,39,536870937]],[logseq____&quot;^15logseq____&quot;,[392,logseq____&quot;^Ulogseq____&quot;,112,536870937]],[logseq____&quot;^15logseq____&quot;,[392,logseq____&quot;^Ulogseq____&quot;,117,536870937]],[logseq____&quot;^15logseq____&quot;,[392,logseq____&quot;^Ulogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[392,logseq____&quot;^Ulogseq____&quot;,119,536870937]],[logseq____&quot;^15logseq____&quot;,[392,logseq____&quot;^Ulogseq____&quot;,122,536870937]],[logseq____&quot;^15logseq____&quot;,[392,logseq____&quot;^17logseq____&quot;,true,536870937]],[logseq____&quot;^15logseq____&quot;,[392,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-29bf-4c4f-a4d4-2342862e25eflogseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[393,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 2a}\\\\quad x\\\\ge-2$\\n\\\\begin{align}\\n|\\\\underbrace{x+2}_{\\\\ge0}logseq____&amp;=x+2\\\\\\\\\\n-x+3logseq____&amp;\\\\le x+2 logseq____&amp;|logseq____&amp; -2\\\\\\\\\\n-x+1logseq____&amp;\\\\le x logseq____&amp;|logseq____&amp; +x\\\\\\\\\\n\\\\frac12logseq____&amp;\\\\le x logseq____&amp;|logseq____&amp; :2\\\\\\\\\\n\\\\end{align}\\n\\\\begin{align}\\nL_2=\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|xlogseq____&lt;3,x\\\\ge-2,x\\\\ge\\\\frac12\\\\right\\\\}=\\\\left[\\\\frac12,3\\\\right)\\n\\\\end{align}logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[393,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[393,logseq____&quot;^Flogseq____&quot;,429,536870937]],[logseq____&quot;^15logseq____&quot;,[393,logseq____&quot;^Xlogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[393,logseq____&quot;^Vlogseq____&quot;,396,536870937]],[logseq____&quot;^15logseq____&quot;,[393,logseq____&quot;^Ulogseq____&quot;,39,536870937]],[logseq____&quot;^15logseq____&quot;,[393,logseq____&quot;^Ulogseq____&quot;,112,536870937]],[logseq____&quot;^15logseq____&quot;,[393,logseq____&quot;^Ulogseq____&quot;,117,536870937]],[logseq____&quot;^15logseq____&quot;,[393,logseq____&quot;^Ulogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[393,logseq____&quot;^Ulogseq____&quot;,119,536870937]],[logseq____&quot;^15logseq____&quot;,[393,logseq____&quot;^Ulogseq____&quot;,122,536870937]],[logseq____&quot;^15logseq____&quot;,[393,logseq____&quot;^17logseq____&quot;,true,536870937]],[logseq____&quot;^15logseq____&quot;,[393,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-88e1-46fc-8f26-9e6cbdf21ba5logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[394,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[394,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[394,logseq____&quot;^Flogseq____&quot;,405,536870937]],[logseq____&quot;^15logseq____&quot;,[394,logseq____&quot;^Xlogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[394,logseq____&quot;^Vlogseq____&quot;,391,536870937]],[logseq____&quot;^15logseq____&quot;,[394,logseq____&quot;^Ulogseq____&quot;,39,536870937]],[logseq____&quot;^15logseq____&quot;,[394,logseq____&quot;^Ulogseq____&quot;,117,536870937]],[logseq____&quot;^15logseq____&quot;,[394,logseq____&quot;^Ulogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[394,logseq____&quot;^Ulogseq____&quot;,119,536870937]],[logseq____&quot;^15logseq____&quot;,[394,logseq____&quot;^Ulogseq____&quot;,122,536870937]],[logseq____&quot;^15logseq____&quot;,[394,logseq____&quot;^Hlogseq____&quot;,39,536870937]],[logseq____&quot;^15logseq____&quot;,[394,logseq____&quot;^17logseq____&quot;,true,536870937]],[logseq____&quot;^15logseq____&quot;,[394,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-3ee6-4805-9e74-c88eef0fcb2elogseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[395,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[395,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[395,logseq____&quot;^Flogseq____&quot;,399,536870937]],[logseq____&quot;^15logseq____&quot;,[395,logseq____&quot;^Xlogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[395,logseq____&quot;^Vlogseq____&quot;,399,536870937]],[logseq____&quot;^15logseq____&quot;,[395,logseq____&quot;^Ulogseq____&quot;,39,536870937]],[logseq____&quot;^15logseq____&quot;,[395,logseq____&quot;^Ulogseq____&quot;,112,536870937]],[logseq____&quot;^15logseq____&quot;,[395,logseq____&quot;^Ulogseq____&quot;,117,536870937]],[logseq____&quot;^15logseq____&quot;,[395,logseq____&quot;^Ulogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[395,logseq____&quot;^Ulogseq____&quot;,119,536870937]],[logseq____&quot;^15logseq____&quot;,[395,logseq____&quot;^Ulogseq____&quot;,122,536870937]],[logseq____&quot;^15logseq____&quot;,[395,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870937]],[logseq____&quot;^15logseq____&quot;,[395,logseq____&quot;^Jlogseq____&quot;,[],536870937]],[logseq____&quot;^15logseq____&quot;,[395,logseq____&quot;^Hlogseq____&quot;,112,536870937]],[logseq____&quot;^15logseq____&quot;,[395,logseq____&quot;^17logseq____&quot;,true,536870937]],[logseq____&quot;^15logseq____&quot;,[395,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-94dd-4916-b573-81377f2955belogseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[396,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[396,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[396,logseq____&quot;^Flogseq____&quot;,420,536870937]],[logseq____&quot;^15logseq____&quot;,[396,logseq____&quot;^Xlogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[396,logseq____&quot;^Vlogseq____&quot;,420,536870937]],[logseq____&quot;^15logseq____&quot;,[396,logseq____&quot;^Ulogseq____&quot;,39,536870937]],[logseq____&quot;^15logseq____&quot;,[396,logseq____&quot;^Ulogseq____&quot;,112,536870937]],[logseq____&quot;^15logseq____&quot;,[396,logseq____&quot;^Ulogseq____&quot;,117,536870937]],[logseq____&quot;^15logseq____&quot;,[396,logseq____&quot;^Ulogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[396,logseq____&quot;^Ulogseq____&quot;,119,536870937]],[logseq____&quot;^15logseq____&quot;,[396,logseq____&quot;^Ulogseq____&quot;,122,536870937]],[logseq____&quot;^15logseq____&quot;,[396,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870937]],[logseq____&quot;^15logseq____&quot;,[396,logseq____&quot;^Jlogseq____&quot;,[],536870937]],[logseq____&quot;^15logseq____&quot;,[396,logseq____&quot;^Hlogseq____&quot;,112,536870937]],[logseq____&quot;^15logseq____&quot;,[396,logseq____&quot;^17logseq____&quot;,true,536870937]],[logseq____&quot;^15logseq____&quot;,[396,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-904b-40a8-b53b-44a5d97bdd5flogseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[397,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Lösungsmenge der Gleichung }x^2+\\\\underbrace{4}_p x-\\\\underbrace{12}_q=0$\\n\\\\begin{align}\\nx_{1,2}logseq____&amp;=\\\\frac{-p}2\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}\\\\\\\\\\nlogseq____&amp;=-2\\\\pm\\\\sqrt{\\\\frac{16}4-(-12)}\\\\\\\\\\nlogseq____&amp;=-2\\\\pm4\\\\\\\\\\nLlogseq____&amp;=\\\\left\\\\{\\\\underbrace{x\\\\in\\\\Reals}_\\\\text{Name}\\\\middle|\\\\underbrace{x^2+4x-12=0}_\\\\text{Eigenschaft}\\\\right\\\\}\\\\\\\\\\nLlogseq____&amp;=\\\\left\\\\{2,-6\\\\right\\\\}\\n\\\\end{align}logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[397,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[397,logseq____&quot;^Flogseq____&quot;,408,536870937]],[logseq____&quot;^15logseq____&quot;,[397,logseq____&quot;^Xlogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[397,logseq____&quot;^Vlogseq____&quot;,408,536870937]],[logseq____&quot;^15logseq____&quot;,[397,logseq____&quot;^Ulogseq____&quot;,115,536870937]],[logseq____&quot;^15logseq____&quot;,[397,logseq____&quot;^Ulogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[397,logseq____&quot;^Ulogseq____&quot;,122,536870937]],[logseq____&quot;^15logseq____&quot;,[397,logseq____&quot;^17logseq____&quot;,true,536870937]],[logseq____&quot;^15logseq____&quot;,[397,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-a067-4d83-8671-0c048580f5b3logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[398,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 2}\\\\quad -5\\\\le xlogseq____&lt;3$\\n\\\\begin{align}\\nx+5logseq____&amp;\\\\le0\\\\\\\\\\n|x+5|logseq____&amp;=x+5\\\\\\\\\\nx-3logseq____&amp;logseq____&lt;0\\\\\\\\\\n|x-3|logseq____&amp;=-(x-3)=-x+3\\\\\\\\\\nx+5logseq____&amp;logseq____&lt;2(-x+3)\\\\\\\\\\nx+5logseq____&amp;logseq____&lt;-2x+6 logseq____&amp;|logseq____&amp;+2x\\\\\\\\\\n3xlogseq____&amp;logseq____&lt;1 logseq____&amp;|logseq____&amp; :3\\\\\\\\\\nxlogseq____&amp;logseq____&lt;\\\\frac13\\n\\\\end{align}\\n\\\\begin{align}\\nL_2=\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-5\\\\le xlogseq____&lt;3,xlogseq____&lt;\\\\frac13\\\\right\\\\}\\n\\\\end{align}logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[398,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[398,logseq____&quot;^Flogseq____&quot;,401,536870937]],[logseq____&quot;^15logseq____&quot;,[398,logseq____&quot;^Xlogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[398,logseq____&quot;^Vlogseq____&quot;,395,536870937]],[logseq____&quot;^15logseq____&quot;,[398,logseq____&quot;^Ulogseq____&quot;,39,536870937]],[logseq____&quot;^15logseq____&quot;,[398,logseq____&quot;^Ulogseq____&quot;,112,536870937]],[logseq____&quot;^15logseq____&quot;,[398,logseq____&quot;^Ulogseq____&quot;,117,536870937]],[logseq____&quot;^15logseq____&quot;,[398,logseq____&quot;^Ulogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[398,logseq____&quot;^Ulogseq____&quot;,119,536870937]],[logseq____&quot;^15logseq____&quot;,[398,logseq____&quot;^Ulogseq____&quot;,122,536870937]],[logseq____&quot;^15logseq____&quot;,[398,logseq____&quot;^17logseq____&quot;,true,536870937]],[logseq____&quot;^15logseq____&quot;,[398,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-959e-473e-897c-e05c73af99falogseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[399,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{gather}\\n\\\\frac{|x+5|}{|x-3|}logseq____&lt;2\\\\quad\\\\Bigm|*|x-3|\\\\qquad x\\\\ne3\\\\\\\\\\nL=\\\\left\\\\{ x\\\\in \\\\Reals \\\\Big| |x+5|logseq____&lt;2|x-3|\\\\right\\\\}\\\\\\\\\\n\\\\end{gather}logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[399,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[399,logseq____&quot;^Flogseq____&quot;,420,536870937]],[logseq____&quot;^15logseq____&quot;,[399,logseq____&quot;^Xlogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[399,logseq____&quot;^Vlogseq____&quot;,394,536870937]],[logseq____&quot;^15logseq____&quot;,[399,logseq____&quot;^Ulogseq____&quot;,39,536870937]],[logseq____&quot;^15logseq____&quot;,[399,logseq____&quot;^Ulogseq____&quot;,117,536870937]],[logseq____&quot;^15logseq____&quot;,[399,logseq____&quot;^Ulogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[399,logseq____&quot;^Ulogseq____&quot;,119,536870937]],[logseq____&quot;^15logseq____&quot;,[399,logseq____&quot;^Ulogseq____&quot;,122,536870937]],[logseq____&quot;^15logseq____&quot;,[399,logseq____&quot;^17logseq____&quot;,true,536870937]],[logseq____&quot;^15logseq____&quot;,[399,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-436d-4507-8ccc-53006284632dlogseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[400,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 1}\\\\quad 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von [Punkten]([[Punkte]]) $(x,y)$ in der [Ebene]([[Ebenen]])  die den gleichen [[Abstand]] r ([[Radius]]) zu einem festen [Punkt]([[Punkte]]) 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Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[414,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[414,logseq____&quot;^Flogseq____&quot;,434,536870937]],[logseq____&quot;^15logseq____&quot;,[414,logseq____&quot;^Xlogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[414,logseq____&quot;^Vlogseq____&quot;,434,536870937]],[logseq____&quot;^15logseq____&quot;,[414,logseq____&quot;^Ulogseq____&quot;,39,536870937]],[logseq____&quot;^15logseq____&quot;,[414,logseq____&quot;^Ulogseq____&quot;,112,536870937]],[logseq____&quot;^15logseq____&quot;,[414,logseq____&quot;^Ulogseq____&quot;,117,536870937]],[logseq____&quot;^15logseq____&quot;,[414,logseq____&quot;^Ulogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[414,logseq____&quot;^Ulogseq____&quot;,119,536870937]],[logseq____&quot;^15logseq____&quot;,[414,logseq____&quot;^Ulogseq____&quot;,122,536870937]],[logseq____&quot;^15logseq____&quot;,[414,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870937]],[logseq____&quot;^15logseq____&quot;,[414,logseq____&quot;^Jlogseq____&quot;,[],536870937]],[logseq____&quot;^15logseq____&quot;,[414,logseq____&quot;^Hlogseq____&quot;,112,536870937]],[logseq____&quot;^15logseq____&quot;,[414,logseq____&quot;^17logseq____&quot;,true,536870937]],[logseq____&quot;^15logseq____&quot;,[414,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-7d3b-4612-925c-788e8f5c5da4logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[415,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 1a}\\\\quad x\\\\ge -2$\\n\\\\begin{align}\\n|x+2|logseq____&amp;=x+2\\\\\\\\\\nx-3logseq____&amp;\\\\le x+2 logseq____&amp;|logseq____&amp;+3-x\\\\\\\\\\n0logseq____&amp;\\\\le5\\\\\\\\\\n\\\\end{align}\\n\\\\begin{align}\\nL_1=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|x\\\\ge3,x\\\\ge-2,0\\\\le5\\\\right\\\\}=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|x\\\\ge3\\\\right\\\\}=[3,\\\\infty)\\n\\\\end{align}logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[415,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[415,logseq____&quot;^Flogseq____&quot;,400,536870937]],[logseq____&quot;^15logseq____&quot;,[415,logseq____&quot;^Xlogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[415,logseq____&quot;^Vlogseq____&quot;,396,536870937]],[logseq____&quot;^15logseq____&quot;,[415,logseq____&quot;^Ulogseq____&quot;,39,536870937]],[logseq____&quot;^15logseq____&quot;,[415,logseq____&quot;^Ulogseq____&quot;,112,536870937]],[logseq____&quot;^15logseq____&quot;,[415,logseq____&quot;^Ulogseq____&quot;,117,536870937]],[logseq____&quot;^15logseq____&quot;,[415,logseq____&quot;^Ulogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[415,logseq____&quot;^Ulogseq____&quot;,119,536870937]],[logseq____&quot;^15logseq____&quot;,[415,logseq____&quot;^Ulogseq____&quot;,122,536870937]],[logseq____&quot;^15logseq____&quot;,[415,logseq____&quot;^17logseq____&quot;,true,536870937]],[logseq____&quot;^15logseq____&quot;,[415,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-9cd2-4f9f-92b8-ce8cc1123d89logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[416,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;**oder** $\\\\rightarrow$ 5 ist abstand von x zu 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incompletelogseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[417,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[417,logseq____&quot;^Flogseq____&quot;,404,536870937]],[logseq____&quot;^15logseq____&quot;,[417,logseq____&quot;^Xlogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[417,logseq____&quot;^Vlogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[417,logseq____&quot;^Ulogseq____&quot;,46,536870937]],[logseq____&quot;^15logseq____&quot;,[417,logseq____&quot;^Ulogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[417,logseq____&quot;^Hlogseq____&quot;,46,536870937]],[logseq____&quot;^15logseq____&quot;,[417,logseq____&quot;^17logseq____&quot;,true,536870937]],[logseq____&quot;^15logseq____&quot;,[417,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-353b-40b2-9d60-ae2732a330ddlogseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[418,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 2}\\\\quad x\\\\ge3$\\n\\\\begin{align}\\n|x-3|logseq____&amp;=-x+3\\\\\\\\\\nx-3logseq____&amp;logseq____&lt;5 logseq____&amp;|logseq____&amp;+3\\\\\\\\\\nxlogseq____&amp;logseq____&lt;8\\\\\\\\\\nL_2logseq____&amp;=[3,8)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[418,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[418,logseq____&quot;^Flogseq____&quot;,392,536870937]],[logseq____&quot;^15logseq____&quot;,[418,logseq____&quot;^Xlogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[418,logseq____&quot;^Vlogseq____&quot;,414,536870937]],[logseq____&quot;^15logseq____&quot;,[418,logseq____&quot;^Ulogseq____&quot;,39,536870937]],[logseq____&quot;^15logseq____&quot;,[418,logseq____&quot;^Ulogseq____&quot;,112,536870937]],[logseq____&quot;^15logseq____&quot;,[418,logseq____&quot;^Ulogseq____&quot;,117,536870937]],[logseq____&quot;^15logseq____&quot;,[418,logseq____&quot;^Ulogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[418,logseq____&quot;^Ulogseq____&quot;,119,536870937]],[logseq____&quot;^15logseq____&quot;,[418,logseq____&quot;^Ulogseq____&quot;,122,536870937]],[logseq____&quot;^15logseq____&quot;,[418,logseq____&quot;^17logseq____&quot;,true,536870937]],[logseq____&quot;^15logseq____&quot;,[418,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-a374-4a2f-a4eb-158a22527f08logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[419,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Der [[Betrag]] ist der zu [[Abstand]] 0\\n\\\\begin{align}\\nf(x)=logseq____&amp;|x|:=logseq____&amp;\\\\begin{cases}\\nxlogseq____&amp;x\\\\ge0\\\\\\\\\\n-xlogseq____&amp;xlogseq____&lt;0\\n\\\\end{cases}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[419,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[419,logseq____&quot;^Flogseq____&quot;,403,536870937]],[logseq____&quot;^15logseq____&quot;,[419,logseq____&quot;^Xlogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[419,logseq____&quot;^Vlogseq____&quot;,403,536870937]],[logseq____&quot;^15logseq____&quot;,[419,logseq____&quot;^Ulogseq____&quot;,116,536870937]],[logseq____&quot;^15logseq____&quot;,[419,logseq____&quot;^Ulogseq____&quot;,117,536870937]],[logseq____&quot;^15logseq____&quot;,[419,logseq____&quot;^Ulogseq____&quot;,118,536870937]],[logseq____&quot;^15logseq____&quot;,[419,logseq____&quot;^Ulogseq____&quot;,122,536870937]],[logseq____&quot;^15logseq____&quot;,[419,logseq____&quot;^Hlogseq____&quot;,116,536870937]],[logseq____&quot;^15logseq____&quot;,[419,logseq____&quot;^Hlogseq____&quot;,117,536870937]],[logseq____&quot;^15logseq____&quot;,[419,logseq____&quot;^17logseq____&quot;,true,536870937]],[logseq____&quot;^15logseq____&quot;,[419,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-823a-4b5a-9478-967f45200c4elogseq____&quot;,536870937]],[logseq____&quot;^15logseq____&quot;,[420,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$$L=\\\\left\\\\{\\\\underbrace{x\\\\in\\\\Reals}_{0\\\\notin 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2b}\\\\quad xlogseq____&lt;-2$\\n\\\\begin{align}\\n|\\\\underbrace{x+2}_{logseq____&lt;0}logseq____&amp;=-(x+2)=-x-2\\\\\\\\\\n-x+3logseq____&amp;\\\\le -x-2 logseq____&amp;|logseq____&amp;+x\\\\\\\\\\n3logseq____&amp;\\\\le-2logseq____&amp;logseq____&amp;\\\\underset{falsche 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[[Beispiele]]logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[441,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[441,logseq____&quot;^Flogseq____&quot;,449,536870939]],[logseq____&quot;^15logseq____&quot;,[441,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[441,logseq____&quot;^Vlogseq____&quot;,450,536870939]],[logseq____&quot;^15logseq____&quot;,[441,logseq____&quot;^Ulogseq____&quot;,39,536870939]],[logseq____&quot;^15logseq____&quot;,[441,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[441,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[441,logseq____&quot;^Ulogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[441,logseq____&quot;^Hlogseq____&quot;,39,536870939]],[logseq____&quot;^15logseq____&quot;,[441,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[441,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-4b0f-455e-9e56-f19899c70052logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[442,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Tantologie]]logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[442,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[442,logseq____&quot;^Flogseq____&quot;,446,536870939]],[logseq____&quot;^15logseq____&quot;,[442,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[442,logseq____&quot;^Vlogseq____&quot;,450,536870939]],[logseq____&quot;^15logseq____&quot;,[442,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[442,logseq____&quot;^Ulogseq____&quot;,178,536870939]],[logseq____&quot;^15logseq____&quot;,[442,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[442,logseq____&quot;^Ulogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[442,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Aussageformel]]logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[446,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[446,logseq____&quot;^Flogseq____&quot;,460,536870939]],[logseq____&quot;^15logseq____&quot;,[446,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[446,logseq____&quot;^Vlogseq____&quot;,450,536870939]],[logseq____&quot;^15logseq____&quot;,[446,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[446,logseq____&quot;^Ulogseq____&quot;,172,536870939]],[logseq____&quot;^15logseq____&quot;,[446,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[446,logseq____&quot;^Ulogseq____&quot;,186,536870939]],[logseq____&quot;^15logseq____&quot;,[446,logseq____&quot;^Ulogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[446,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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istlogseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[447,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[447,logseq____&quot;^Flogseq____&quot;,444,536870939]],[logseq____&quot;^15logseq____&quot;,[447,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[447,logseq____&quot;^Vlogseq____&quot;,444,536870939]],[logseq____&quot;^15logseq____&quot;,[447,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[447,logseq____&quot;^Ulogseq____&quot;,179,536870939]],[logseq____&quot;^15logseq____&quot;,[447,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[447,logseq____&quot;^Ulogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[447,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[447,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-51b5-402e-9a75-02a19ed4b285logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[448,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[448,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[448,logseq____&quot;^Flogseq____&quot;,451,536870939]],[logseq____&quot;^15logseq____&quot;,[448,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[448,logseq____&quot;^Vlogseq____&quot;,450,536870939]],[logseq____&quot;^15logseq____&quot;,[448,logseq____&quot;^Ulogseq____&quot;,39,536870939]],[logseq____&quot;^15logseq____&quot;,[448,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[448,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[448,logseq____&quot;^Ulogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[448,logseq____&quot;^Hlogseq____&quot;,39,536870939]],[logseq____&quot;^15logseq____&quot;,[448,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[448,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-71cb-4721-9eed-b69ec562d7c0logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[449,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[449,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[449,logseq____&quot;^Flogseq____&quot;,465,536870939]],[logseq____&quot;^15logseq____&quot;,[449,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[449,logseq____&quot;^Vlogseq____&quot;,450,536870939]],[logseq____&quot;^15logseq____&quot;,[449,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[449,logseq____&quot;^Ulogseq____&quot;,178,536870939]],[logseq____&quot;^15logseq____&quot;,[449,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[449,logseq____&quot;^Ulogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[449,logseq____&quot;^Hlogseq____&quot;,178,536870939]],[logseq____&quot;^15logseq____&quot;,[449,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[449,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-c6e3-4f5d-9c0e-470a697a50d8logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[450,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Verknüpfung von Aussagen]]logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[450,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[450,logseq____&quot;^Flogseq____&quot;,462,536870939]],[logseq____&quot;^15logseq____&quot;,[450,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[450,logseq____&quot;^Vlogseq____&quot;,445,536870939]],[logseq____&quot;^15logseq____&quot;,[450,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[450,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[450,logseq____&quot;^Ulogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[450,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870939]],[logseq____&quot;^15logseq____&quot;,[450,logseq____&quot;^Jlogseq____&quot;,[],536870939]],[logseq____&quot;^15logseq____&quot;,[450,logseq____&quot;^Hlogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[450,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[450,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-1776-4cb5-b5ac-a5b69ec8d3f8logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[451,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sind $p$ und $q$ [[Aussagen]], so auch\\n\\\\begin{align}\\n(p\\\\land q) logseq____&amp;\\\\quadlogseq____&amp; (\\logseq____&quot;\\\\text{und}\\logseq____&quot;)\\\\\\\\\\n(p\\\\lor q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{oder}\\logseq____&quot;)\\\\\\\\\\n(\\\\neg p) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{nicht}\\logseq____&quot;)\\\\\\\\\\n(p\\\\rightarrow q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{impliziert}\\logseq____&quot;)\\\\\\\\\\n(p\\\\leftrightarrow q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{genau dann wenn}\\logseq____&quot;)\\n\\\\end{align}logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[451,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[451,logseq____&quot;^Flogseq____&quot;,450,536870939]],[logseq____&quot;^15logseq____&quot;,[451,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[451,logseq____&quot;^Vlogseq____&quot;,450,536870939]],[logseq____&quot;^15logseq____&quot;,[451,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[451,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[451,logseq____&quot;^Ulogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[451,logseq____&quot;^Hlogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[451,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[451,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-8151-4085-aedd-9865894318e1logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[452,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussagenlogische Variable]]logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[452,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[452,logseq____&quot;^Flogseq____&quot;,461,536870939]],[logseq____&quot;^15logseq____&quot;,[452,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[452,logseq____&quot;^Vlogseq____&quot;,450,536870939]],[logseq____&quot;^15logseq____&quot;,[452,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[452,logseq____&quot;^Ulogseq____&quot;,173,536870939]],[logseq____&quot;^15logseq____&quot;,[452,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[452,logseq____&quot;^Ulogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[452,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870939]],[logseq____&quot;^15logseq____&quot;,[452,logseq____&quot;^Jlogseq____&quot;,[],536870939]],[logseq____&quot;^15logseq____&quot;,[452,logseq____&quot;^Hlogseq____&quot;,173,536870939]],[logseq____&quot;^15logseq____&quot;,[452,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[452,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-f262-43ad-a4f8-857b67951e66logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[453,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Variable]([[Variablen]]), die den Wert $w$ oder $f$ annimmtlogseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[453,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[453,logseq____&quot;^Flogseq____&quot;,452,536870939]],[logseq____&quot;^15logseq____&quot;,[453,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[453,logseq____&quot;^Vlogseq____&quot;,452,536870939]],[logseq____&quot;^15logseq____&quot;,[453,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[453,logseq____&quot;^Ulogseq____&quot;,173,536870939]],[logseq____&quot;^15logseq____&quot;,[453,logseq____&quot;^Ulogseq____&quot;,180,536870939]],[logseq____&quot;^15logseq____&quot;,[453,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[453,logseq____&quot;^Ulogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[453,logseq____&quot;^Hlogseq____&quot;,180,536870939]],[logseq____&quot;^15logseq____&quot;,[453,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[453,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-1352-40a3-9a9b-451846273363logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[454,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wikipedia]]logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[454,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[454,logseq____&quot;^Flogseq____&quot;,457,536870939]],[logseq____&quot;^15logseq____&quot;,[454,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[454,logseq____&quot;^Vlogseq____&quot;,438,536870939]],[logseq____&quot;^15logseq____&quot;,[454,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[454,logseq____&quot;^Ulogseq____&quot;,174,536870939]],[logseq____&quot;^15logseq____&quot;,[454,logseq____&quot;^Hlogseq____&quot;,174,536870939]],[logseq____&quot;^15logseq____&quot;,[454,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[454,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-a3e1-4e34-a119-0b69cc7af410logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[455,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussageformel]]logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[455,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[455,logseq____&quot;^Flogseq____&quot;,452,536870939]],[logseq____&quot;^15logseq____&quot;,[455,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[455,logseq____&quot;^Vlogseq____&quot;,450,536870939]],[logseq____&quot;^15logseq____&quot;,[455,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[455,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[455,logseq____&quot;^Ulogseq____&quot;,186,536870939]],[logseq____&quot;^15logseq____&quot;,[455,logseq____&quot;^Ulogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[455,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870939]],[logseq____&quot;^15logseq____&quot;,[455,logseq____&quot;^Jlogseq____&quot;,[],536870939]],[logseq____&quot;^15logseq____&quot;,[455,logseq____&quot;^Hlogseq____&quot;,186,536870939]],[logseq____&quot;^15logseq____&quot;,[455,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[455,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-e5b1-4ebe-ac36-fd3f0ee2b313logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[456,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Zuordnung von $w/f$ an jede [Variable]([[Variablen]]) einer [[Aussageformel]]logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[456,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[456,logseq____&quot;^Flogseq____&quot;,460,536870939]],[logseq____&quot;^15logseq____&quot;,[456,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[456,logseq____&quot;^Vlogseq____&quot;,460,536870939]],[logseq____&quot;^15logseq____&quot;,[456,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[456,logseq____&quot;^Ulogseq____&quot;,180,536870939]],[logseq____&quot;^15logseq____&quot;,[456,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[456,logseq____&quot;^Ulogseq____&quot;,186,536870939]],[logseq____&quot;^15logseq____&quot;,[456,logseq____&quot;^Ulogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[456,logseq____&quot;^Ulogseq____&quot;,190,536870939]],[logseq____&quot;^15logseq____&quot;,[456,logseq____&quot;^Hlogseq____&quot;,180,536870939]],[logseq____&quot;^15logseq____&quot;,[456,logseq____&quot;^Hlogseq____&quot;,186,536870939]],[logseq____&quot;^15logseq____&quot;,[456,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[456,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-5b58-4165-b03f-88f0d039730clogseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[457,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;C. Meinel, M. Mundhenk,  [[\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. Auflage 2011]]logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[457,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[457,logseq____&quot;^Flogseq____&quot;,438,536870939]],[logseq____&quot;^15logseq____&quot;,[457,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[457,logseq____&quot;^Vlogseq____&quot;,438,536870939]],[logseq____&quot;^15logseq____&quot;,[457,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[457,logseq____&quot;^Ulogseq____&quot;,177,536870939]],[logseq____&quot;^15logseq____&quot;,[457,logseq____&quot;^Hlogseq____&quot;,177,536870939]],[logseq____&quot;^15logseq____&quot;,[457,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[457,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-4f37-48fd-863b-9d851e906248logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^Flogseq____&quot;,446,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^Vlogseq____&quot;,446,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^Ulogseq____&quot;,172,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^Ulogseq____&quot;,175,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^Ulogseq____&quot;,176,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^Ulogseq____&quot;,183,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^Ulogseq____&quot;,186,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^Ulogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^Ulogseq____&quot;,190,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^Hlogseq____&quot;,175,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^Hlogseq____&quot;,176,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^Hlogseq____&quot;,183,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^Hlogseq____&quot;,190,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[458,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-10f1-4e6d-be19-ecad22a41ce2logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[459,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\np\\\\land q\\\\lor r\\\\\\\\\\n(p\\\\land q)\\\\lor r\\\\\\\\\\np\\\\land (q\\\\lor r)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[459,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[459,logseq____&quot;^Flogseq____&quot;,448,536870939]],[logseq____&quot;^15logseq____&quot;,[459,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[459,logseq____&quot;^Vlogseq____&quot;,448,536870939]],[logseq____&quot;^15logseq____&quot;,[459,logseq____&quot;^Ulogseq____&quot;,39,536870939]],[logseq____&quot;^15logseq____&quot;,[459,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[459,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[459,logseq____&quot;^Ulogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[459,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[459,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-dddd-4681-bf79-fb68953d55fdlogseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[460,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Belegung]] (der [[Variablen]])logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[460,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[460,logseq____&quot;^Flogseq____&quot;,455,536870939]],[logseq____&quot;^15logseq____&quot;,[460,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[460,logseq____&quot;^Vlogseq____&quot;,450,536870939]],[logseq____&quot;^15logseq____&quot;,[460,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[460,logseq____&quot;^Ulogseq____&quot;,180,536870939]],[logseq____&quot;^15logseq____&quot;,[460,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[460,logseq____&quot;^Ulogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[460,logseq____&quot;^Ulogseq____&quot;,190,536870939]],[logseq____&quot;^15logseq____&quot;,[460,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870939]],[logseq____&quot;^15logseq____&quot;,[460,logseq____&quot;^Jlogseq____&quot;,[],536870939]],[logseq____&quot;^15logseq____&quot;,[460,logseq____&quot;^Hlogseq____&quot;,180,536870939]],[logseq____&quot;^15logseq____&quot;,[460,logseq____&quot;^Hlogseq____&quot;,190,536870939]],[logseq____&quot;^15logseq____&quot;,[460,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[460,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-6144-494b-91c3-87800fd85a5elogseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[461,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Soweit die \\logseq____&quot;[[Syntax]]\\logseq____&quot;, jetzt die [[Semantik]]. Die [Wahrheitswerte]([[Wahrheitswert]])\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[461,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[461,logseq____&quot;^Flogseq____&quot;,448,536870939]],[logseq____&quot;^15logseq____&quot;,[461,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[461,logseq____&quot;^Vlogseq____&quot;,450,536870939]],[logseq____&quot;^15logseq____&quot;,[461,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[461,logseq____&quot;^Ulogseq____&quot;,176,536870939]],[logseq____&quot;^15logseq____&quot;,[461,logseq____&quot;^Ulogseq____&quot;,181,536870939]],[logseq____&quot;^15logseq____&quot;,[461,logseq____&quot;^Ulogseq____&quot;,183,536870939]],[logseq____&quot;^15logseq____&quot;,[461,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[461,logseq____&quot;^Ulogseq____&quot;,187,536870939]],[logseq____&quot;^15logseq____&quot;,[461,logseq____&quot;^Ulogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[461,logseq____&quot;^Hlogseq____&quot;,176,536870939]],[logseq____&quot;^15logseq____&quot;,[461,logseq____&quot;^Hlogseq____&quot;,181,536870939]],[logseq____&quot;^15logseq____&quot;,[461,logseq____&quot;^Hlogseq____&quot;,183,536870939]],[logseq____&quot;^15logseq____&quot;,[461,logseq____&quot;^Hlogseq____&quot;,187,536870939]],[logseq____&quot;^15logseq____&quot;,[461,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[461,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-cc6e-475a-a244-d80315c0f0f1logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[462,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\nlogseq____&amp;\\logseq____&quot;5\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;\\\\quadlogseq____&amp; (w)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;4\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;logseq____&amp; (f)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Jede gerade Zahl }\\\\ge4\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ ist Summe zweier Primzahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage, }w\\\\text{ oder }f)\\\\notag\\\\\\\\\\nlogseq____&amp;(\\\\text{Vermutung von Goldback 1742})\\\\text{, }logseq____&amp;logseq____&amp;\\\\text{richtig für gerade Zahlen bis }4*10^{18}\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Dieser Satz ist falsch}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{keine Aussage})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Gleichung } x^2+y^2=z^2 \\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ hat eine Lösung }x,y,z\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nlogseq____&amp;x^n+y^n=z^n\\\\text{ eine Lösung}logseq____&amp;logseq____&amp; (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nlogseq____&amp;x,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp;\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Gott ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Nietzsche ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[462,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[462,logseq____&quot;^Flogseq____&quot;,443,536870939]],[logseq____&quot;^15logseq____&quot;,[462,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[462,logseq____&quot;^Vlogseq____&quot;,445,536870939]],[logseq____&quot;^15logseq____&quot;,[462,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[462,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[462,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[462,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-d1ad-4f8e-a062-c43d7f73ad06logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[463,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[463,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[463,logseq____&quot;^Flogseq____&quot;,455,536870939]],[logseq____&quot;^15logseq____&quot;,[463,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[463,logseq____&quot;^Vlogseq____&quot;,455,536870939]],[logseq____&quot;^15logseq____&quot;,[463,logseq____&quot;^Ulogseq____&quot;,46,536870939]],[logseq____&quot;^15logseq____&quot;,[463,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[463,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[463,logseq____&quot;^Ulogseq____&quot;,185,536870939]],[logseq____&quot;^15logseq____&quot;,[463,logseq____&quot;^Ulogseq____&quot;,186,536870939]],[logseq____&quot;^15logseq____&quot;,[463,logseq____&quot;^Ulogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[463,logseq____&quot;^Hlogseq____&quot;,46,536870939]],[logseq____&quot;^15logseq____&quot;,[463,logseq____&quot;^Hlogseq____&quot;,185,536870939]],[logseq____&quot;^15logseq____&quot;,[463,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[463,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-4471-4607-badc-dd926e52133dlogseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[464,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $w$ istlogseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[464,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[464,logseq____&quot;^Flogseq____&quot;,442,536870939]],[logseq____&quot;^15logseq____&quot;,[464,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[464,logseq____&quot;^Vlogseq____&quot;,442,536870939]],[logseq____&quot;^15logseq____&quot;,[464,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[464,logseq____&quot;^Ulogseq____&quot;,178,536870939]],[logseq____&quot;^15logseq____&quot;,[464,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[464,logseq____&quot;^Ulogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[464,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[464,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-5669-4318-bab1-02f88e8fd1a7logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[465,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formeln $p,q$ [logisch äquivalent]([[Logisch Äquivalent]]), wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[465,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[465,logseq____&quot;^Flogseq____&quot;,444,536870939]],[logseq____&quot;^15logseq____&quot;,[465,logseq____&quot;^Xlogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[465,logseq____&quot;^Vlogseq____&quot;,450,536870939]],[logseq____&quot;^15logseq____&quot;,[465,logseq____&quot;^Ulogseq____&quot;,169,536870939]],[logseq____&quot;^15logseq____&quot;,[465,logseq____&quot;^Ulogseq____&quot;,172,536870939]],[logseq____&quot;^15logseq____&quot;,[465,logseq____&quot;^Ulogseq____&quot;,182,536870939]],[logseq____&quot;^15logseq____&quot;,[465,logseq____&quot;^Ulogseq____&quot;,184,536870939]],[logseq____&quot;^15logseq____&quot;,[465,logseq____&quot;^Ulogseq____&quot;,188,536870939]],[logseq____&quot;^15logseq____&quot;,[465,logseq____&quot;^Ulogseq____&quot;,189,536870939]],[logseq____&quot;^15logseq____&quot;,[465,logseq____&quot;^Hlogseq____&quot;,172,536870939]],[logseq____&quot;^15logseq____&quot;,[465,logseq____&quot;^Hlogseq____&quot;,182,536870939]],[logseq____&quot;^15logseq____&quot;,[465,logseq____&quot;^Hlogseq____&quot;,189,536870939]],[logseq____&quot;^15logseq____&quot;,[465,logseq____&quot;^17logseq____&quot;,true,536870939]],[logseq____&quot;^15logseq____&quot;,[465,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf4-bac1-4cb1-8ce8-e8b78f944ca0logseq____&quot;,536870939]],[logseq____&quot;^15logseq____&quot;,[467,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Satz]] mit [[Variablen]] $x_1,\\\\cdots,x_n$, der bei Ersetzung jedes $x_j$ durch ein [Objekt]([[Objekt (Logik)]]) aus $U_j$ stets zu einer [Aussage]([[Aussagen]]) wirdlogseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[467,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[467,logseq____&quot;^Flogseq____&quot;,494,536870940]],[logseq____&quot;^15logseq____&quot;,[467,logseq____&quot;^Xlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[467,logseq____&quot;^Vlogseq____&quot;,478,536870940]],[logseq____&quot;^15logseq____&quot;,[467,logseq____&quot;^Ulogseq____&quot;,180,536870940]],[logseq____&quot;^15logseq____&quot;,[467,logseq____&quot;^Ulogseq____&quot;,184,536870940]],[logseq____&quot;^15logseq____&quot;,[467,logseq____&quot;^Ulogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[467,logseq____&quot;^Ulogseq____&quot;,238,536870940]],[logseq____&quot;^15logseq____&quot;,[467,logseq____&quot;^Ulogseq____&quot;,241,536870940]],[logseq____&quot;^15logseq____&quot;,[467,logseq____&quot;^Ulogseq____&quot;,244,536870940]],[logseq____&quot;^15logseq____&quot;,[467,logseq____&quot;^Hlogseq____&quot;,180,536870940]],[logseq____&quot;^15logseq____&quot;,[467,logseq____&quot;^Hlogseq____&quot;,184,536870940]],[logseq____&quot;^15logseq____&quot;,[467,logseq____&quot;^Hlogseq____&quot;,241,536870940]],[logseq____&quot;^15logseq____&quot;,[467,logseq____&quot;^Hlogseq____&quot;,244,536870940]],[logseq____&quot;^15logseq____&quot;,[467,logseq____&quot;^17logseq____&quot;,true,536870940]],[logseq____&quot;^15logseq____&quot;,[467,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-05e2-416e-9fc5-8bd17b77f89dlogseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[468,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\logseq____&quot;\\\\text{x ist prim}\\logseq____&quot; \\\\quad logseq____&amp; \\\\text{ist AF mit Variablen x über den  natürlichen Zahlen}\\\\\\\\\\n\\logseq____&quot;\\\\underbrace{x}_{x_1}logseq____&lt;\\\\underbrace{y}_{x_2}\\logseq____&quot;\\\\quad logseq____&amp;\\\\text{ist AF mit Variablen }x,y\\\\text{ über die reellen Zahlen } \\\\underbrace{\\\\Reals}_{U_1},\\\\underbrace{\\\\Reals}_{U_2}\\\\\\\\\\n\\logseq____&quot;\\\\text{x ist wahr}\\logseq____&quot;\\\\quadlogseq____&amp;\\\\text{ist AF mit Variablen x über dem Universum der Aussagen}\\n\\\\end{align}logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[468,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[468,logseq____&quot;^Flogseq____&quot;,504,536870940]],[logseq____&quot;^15logseq____&quot;,[468,logseq____&quot;^Xlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[468,logseq____&quot;^Vlogseq____&quot;,478,536870940]],[logseq____&quot;^15logseq____&quot;,[468,logseq____&quot;^Ulogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[468,logseq____&quot;^Ulogseq____&quot;,238,536870940]],[logseq____&quot;^15logseq____&quot;,[468,logseq____&quot;^17logseq____&quot;,true,536870940]],[logseq____&quot;^15logseq____&quot;,[468,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-4cb3-4fea-8657-a8643b797c64logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[469,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist falsch}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[469,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[469,logseq____&quot;^Flogseq____&quot;,492,536870940]],[logseq____&quot;^15logseq____&quot;,[469,logseq____&quot;^Xlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[469,logseq____&quot;^Vlogseq____&quot;,475,536870940]],[logseq____&quot;^15logseq____&quot;,[469,logseq____&quot;^Ulogseq____&quot;,39,536870940]],[logseq____&quot;^15logseq____&quot;,[469,logseq____&quot;^Ulogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[469,logseq____&quot;^Ulogseq____&quot;,228,536870940]],[logseq____&quot;^15logseq____&quot;,[469,logseq____&quot;^Ulogseq____&quot;,231,536870940]],[logseq____&quot;^15logseq____&quot;,[469,logseq____&quot;^Ulogseq____&quot;,232,536870940]],[logseq____&quot;^15logseq____&quot;,[469,logseq____&quot;^Ulogseq____&quot;,238,536870940]],[logseq____&quot;^15logseq____&quot;,[469,logseq____&quot;^Hlogseq____&quot;,231,536870940]],[logseq____&quot;^15logseq____&quot;,[469,logseq____&quot;^17logseq____&quot;,true,536870940]],[logseq____&quot;^15logseq____&quot;,[469,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-bd7f-493a-860e-8397a8d6f8c9logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[470,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Wäre $y$ aus $\\\\Reals$ mit $xlogseq____&lt;y$ für alle $x$ aus $\\\\Reals$, so insbesondere auch $ylogseq____&lt;y$, Widerspruch. $\\\\blacksquare$logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[470,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[470,logseq____&quot;^Flogseq____&quot;,469,536870940]],[logseq____&quot;^15logseq____&quot;,[470,logseq____&quot;^Xlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[470,logseq____&quot;^Vlogseq____&quot;,469,536870940]],[logseq____&quot;^15logseq____&quot;,[470,logseq____&quot;^Ulogseq____&quot;,39,536870940]],[logseq____&quot;^15logseq____&quot;,[470,logseq____&quot;^Ulogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[470,logseq____&quot;^Ulogseq____&quot;,228,536870940]],[logseq____&quot;^15logseq____&quot;,[470,logseq____&quot;^Ulogseq____&quot;,231,536870940]],[logseq____&quot;^15logseq____&quot;,[470,logseq____&quot;^Ulogseq____&quot;,232,536870940]],[logseq____&quot;^15logseq____&quot;,[470,logseq____&quot;^Ulogseq____&quot;,238,536870940]],[logseq____&quot;^15logseq____&quot;,[470,logseq____&quot;^17logseq____&quot;,true,536870940]],[logseq____&quot;^15logseq____&quot;,[470,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-137b-40ea-9a7c-02472802becclogseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[471,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativschreibweisen:\\n$\\\\forall x: p(x)$ auch $\\\\bigwedge x:p(x)$\\n$\\\\exists x:p(x)$ auch $\\\\bigvee x:p(x)$logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[471,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[471,logseq____&quot;^Flogseq____&quot;,498,536870940]],[logseq____&quot;^15logseq____&quot;,[471,logseq____&quot;^Xlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[471,logseq____&quot;^Vlogseq____&quot;,478,536870940]],[logseq____&quot;^15logseq____&quot;,[471,logseq____&quot;^Ulogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[471,logseq____&quot;^Ulogseq____&quot;,238,536870940]],[logseq____&quot;^15logseq____&quot;,[471,logseq____&quot;^17logseq____&quot;,true,536870940]],[logseq____&quot;^15logseq____&quot;,[471,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-d680-4ff1-bae5-d83a52345beelogseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[472,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nlogseq____&amp;\\\\forall x: \\\\forall y: p(x, y) \\\\equiv \\\\forall y: \\\\forall x: p(x,y)\\\\\\\\\\nlogseq____&amp;\\\\exists x:\\\\exists y:p(x,y)\\\\equiv\\\\exists y:\\\\exists x:p(x,y)\\\\\\\\\\nlogseq____&amp;[\\\\forall x_1:\\\\forall x_2: \\\\cdots:\\\\forall x_n:p(x_1,x_2,\\\\cdots,x_n)\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\equiv\\\\forall_{x_{\\\\pi(1)}}:\\\\forall_{x_{\\\\pi(1)}}:\\\\cdots:\\\\forall_{x_{\\\\pi(1)}}:p(x_1,x_2,\\\\cdots,x_n)\\n\\\\end{align}logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[472,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[472,logseq____&quot;^Flogseq____&quot;,474,536870940]],[logseq____&quot;^15logseq____&quot;,[472,logseq____&quot;^Xlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[472,logseq____&quot;^Vlogseq____&quot;,474,536870940]],[logseq____&quot;^15logseq____&quot;,[472,logseq____&quot;^Ulogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[472,logseq____&quot;^Ulogseq____&quot;,228,536870940]],[logseq____&quot;^15logseq____&quot;,[472,logseq____&quot;^Ulogseq____&quot;,232,536870940]],[logseq____&quot;^15logseq____&quot;,[472,logseq____&quot;^Ulogseq____&quot;,238,536870940]],[logseq____&quot;^15logseq____&quot;,[472,logseq____&quot;^17logseq____&quot;,true,536870940]],[logseq____&quot;^15logseq____&quot;,[472,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-83d8-4b84-8535-50d2ae69d6fclogseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[473,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x,y)$ AF in Variablen $x,y$ über $U_1,U_2$\\n\\\\begin{align}\\n\\\\underbrace{\\\\forall x: \\\\underbrace{\\\\exists y: p(x,y)}_{\\\\text{AF in den Variablen }x\\\\text{ über }U_1}}_{\\\\text{Aussage}}\\n\\\\end{align}logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[473,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[473,logseq____&quot;^Flogseq____&quot;,497,536870940]],[logseq____&quot;^15logseq____&quot;,[473,logseq____&quot;^Xlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[473,logseq____&quot;^Vlogseq____&quot;,497,536870940]],[logseq____&quot;^15logseq____&quot;,[473,logseq____&quot;^Ulogseq____&quot;,39,536870940]],[logseq____&quot;^15logseq____&quot;,[473,logseq____&quot;^Ulogseq____&quot;,220,536870940]],[logseq____&quot;^15logseq____&quot;,[473,logseq____&quot;^Ulogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[473,logseq____&quot;^Ulogseq____&quot;,238,536870940]],[logseq____&quot;^15logseq____&quot;,[473,logseq____&quot;^17logseq____&quot;,true,536870940]],[logseq____&quot;^15logseq____&quot;,[473,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-268b-49f4-beb8-be94d2fd890dlogseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[474,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Gleichartige]([[Gleichartig]]) [[Quantoren]] dürfen vertauscht werdenlogseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[474,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[474,logseq____&quot;^Flogseq____&quot;,495,536870940]],[logseq____&quot;^15logseq____&quot;,[474,logseq____&quot;^Xlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[474,logseq____&quot;^Vlogseq____&quot;,478,536870940]],[logseq____&quot;^15logseq____&quot;,[474,logseq____&quot;^Ulogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[474,logseq____&quot;^Ulogseq____&quot;,228,536870940]],[logseq____&quot;^15logseq____&quot;,[474,logseq____&quot;^Ulogseq____&quot;,232,536870940]],[logseq____&quot;^15logseq____&quot;,[474,logseq____&quot;^Ulogseq____&quot;,238,536870940]],[logseq____&quot;^15logseq____&quot;,[474,logseq____&quot;^Hlogseq____&quot;,228,536870940]],[logseq____&quot;^15logseq____&quot;,[474,logseq____&quot;^Hlogseq____&quot;,232,536870940]],[logseq____&quot;^15logseq____&quot;,[474,logseq____&quot;^17logseq____&quot;,true,536870940]],[logseq____&quot;^15logseq____&quot;,[474,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-4763-41b9-a763-26ac51944e91logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[475,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Betrachte $\\logseq____&quot;xlogseq____&lt;y\\logseq____&quot;$ als AF über $\\\\Reals, \\\\Reals$logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[475,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[475,logseq____&quot;^Flogseq____&quot;,486,536870940]],[logseq____&quot;^15logseq____&quot;,[475,logseq____&quot;^Xlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[475,logseq____&quot;^Vlogseq____&quot;,486,536870940]],[logseq____&quot;^15logseq____&quot;,[475,logseq____&quot;^Ulogseq____&quot;,39,536870940]],[logseq____&quot;^15logseq____&quot;,[475,logseq____&quot;^Ulogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[475,logseq____&quot;^Ulogseq____&quot;,228,536870940]],[logseq____&quot;^15logseq____&quot;,[475,logseq____&quot;^Ulogseq____&quot;,232,536870940]],[logseq____&quot;^15logseq____&quot;,[475,logseq____&quot;^Ulogseq____&quot;,238,536870940]],[logseq____&quot;^15logseq____&quot;,[475,logseq____&quot;^17logseq____&quot;,true,536870940]],[logseq____&quot;^15logseq____&quot;,[475,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-4a99-4d3a-8390-094f5fb8900dlogseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[476,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[476,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[476,logseq____&quot;^Flogseq____&quot;,501,536870940]],[logseq____&quot;^15logseq____&quot;,[476,logseq____&quot;^Xlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[476,logseq____&quot;^Vlogseq____&quot;,501,536870940]],[logseq____&quot;^15logseq____&quot;,[476,logseq____&quot;^Ulogseq____&quot;,220,536870940]],[logseq____&quot;^15logseq____&quot;,[476,logseq____&quot;^Ulogseq____&quot;,223,536870940]],[logseq____&quot;^15logseq____&quot;,[476,logseq____&quot;^Ulogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[476,logseq____&quot;^Ulogseq____&quot;,235,536870940]],[logseq____&quot;^15logseq____&quot;,[476,logseq____&quot;^Ulogseq____&quot;,238,536870940]],[logseq____&quot;^15logseq____&quot;,[476,logseq____&quot;^Ulogseq____&quot;,240,536870940]],[logseq____&quot;^15logseq____&quot;,[476,logseq____&quot;^Hlogseq____&quot;,223,536870940]],[logseq____&quot;^15logseq____&quot;,[476,logseq____&quot;^Hlogseq____&quot;,235,536870940]],[logseq____&quot;^15logseq____&quot;,[476,logseq____&quot;^Hlogseq____&quot;,240,536870940]],[logseq____&quot;^15logseq____&quot;,[476,logseq____&quot;^17logseq____&quot;,true,536870940]],[logseq____&quot;^15logseq____&quot;,[476,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-e75b-472a-ad93-de34a607a342logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[477,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n(p\\\\land q)\\\\land r logseq____&amp;\\\\equiv p\\\\land(q\\\\land r),\\\\quadlogseq____&amp;\\\\text{schreibe daher: }  p\\\\land q\\\\land r,\\\\quad \\\\land \\\\text{ assoziativ}\\\\\\\\\\n(p \\\\lor q) \\\\lor r logseq____&amp;\\\\equiv p \\\\lor (q\\\\lor r),\\\\quadlogseq____&amp;\\\\text{schreibe daher: } p\\\\lor q\\\\lor r,\\\\quad \\\\lor \\\\text{ assoziativ}\\\\\\\\\\np \\\\land q logseq____&amp;\\\\equiv q \\\\land p,\\\\quad \\\\land logseq____&amp;\\\\text{ kommutativ}\\\\\\\\\\np \\\\lor q logseq____&amp;\\\\equiv q \\\\lor p,\\\\quad \\\\lor logseq____&amp;\\\\text{ kommutativ}\\\\\\\\\\n\\\\neg(\\\\neg p) logseq____&amp;\\\\equiv p, \\\\quad \\\\neg logseq____&amp;\\\\text{ idenpotent}\\\\\\\\\\np\\\\land(q\\\\lor r)logseq____&amp;\\\\equiv (p\\\\land q)\\\\lor(p\\\\land r);\\\\notag\\\\\\\\\\np\\\\lor(q\\\\land r)logseq____&amp;\\\\equiv (p\\\\lor q)\\\\lor(p\\\\land r),\\\\quad logseq____&amp;\\\\land,\\\\lor\\\\text{ wechselseitig distributiv}\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&amp;\\\\equiv(\\\\neg p)\\\\lor(\\\\neg q);\\\\notag\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&amp;\\\\equiv(\\\\neg p)\\\\land (\\\\neg q), \\\\quad logseq____&amp;\\\\text{ (kleine) de Morgansche Regeln}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[477,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[477,logseq____&quot;^Flogseq____&quot;,489,536870940]],[logseq____&quot;^15logseq____&quot;,[477,logseq____&quot;^Xlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[477,logseq____&quot;^Vlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[477,logseq____&quot;^Ulogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[477,logseq____&quot;^17logseq____&quot;,true,536870940]],[logseq____&quot;^15logseq____&quot;,[477,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-f180-44bd-a647-08c6de301b07logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[478,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Aussageform]]logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[478,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[478,logseq____&quot;^Flogseq____&quot;,477,536870940]],[logseq____&quot;^15logseq____&quot;,[478,logseq____&quot;^Xlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[478,logseq____&quot;^Vlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[478,logseq____&quot;^Ulogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[478,logseq____&quot;^Ulogseq____&quot;,238,536870940]],[logseq____&quot;^15logseq____&quot;,[478,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870940]],[logseq____&quot;^15logseq____&quot;,[478,logseq____&quot;^Jlogseq____&quot;,[],536870940]],[logseq____&quot;^15logseq____&quot;,[478,logseq____&quot;^Hlogseq____&quot;,238,536870940]],[logseq____&quot;^15logseq____&quot;,[478,logseq____&quot;^17logseq____&quot;,true,536870940]],[logseq____&quot;^15logseq____&quot;,[478,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-2bd0-48c9-8d49-14c342821176logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[479,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $x$ aus $\\\\Reals$ beliebig. Setze $y:=x+1$ (ist aus $\\\\Reals$). Dann ist $xlogseq____&lt;x+1=y$ also $xlogseq____&lt;y$. $\\\\blacksquare$logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[479,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[479,logseq____&quot;^Flogseq____&quot;,492,536870940]],[logseq____&quot;^15logseq____&quot;,[479,logseq____&quot;^Xlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[479,logseq____&quot;^Vlogseq____&quot;,492,536870940]],[logseq____&quot;^15logseq____&quot;,[479,logseq____&quot;^Ulogseq____&quot;,39,536870940]],[logseq____&quot;^15logseq____&quot;,[479,logseq____&quot;^Ulogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[479,logseq____&quot;^Ulogseq____&quot;,228,536870940]],[logseq____&quot;^15logseq____&quot;,[479,logseq____&quot;^Ulogseq____&quot;,231,536870940]],[logseq____&quot;^15logseq____&quot;,[479,logseq____&quot;^Ulogseq____&quot;,232,536870940]],[logseq____&quot;^15logseq____&quot;,[479,logseq____&quot;^Ulogseq____&quot;,238,536870940]],[logseq____&quot;^15logseq____&quot;,[479,logseq____&quot;^17logseq____&quot;,true,536870940]],[logseq____&quot;^15logseq____&quot;,[479,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-80e6-485e-88d3-fb30e66572b8logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche Regeln]]logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^Flogseq____&quot;,477,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^Xlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^Vlogseq____&quot;,477,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^Ulogseq____&quot;,221,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^Ulogseq____&quot;,226,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^Ulogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^Ulogseq____&quot;,229,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^Ulogseq____&quot;,230,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^Ulogseq____&quot;,236,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^Ulogseq____&quot;,237,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^Hlogseq____&quot;,221,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^Hlogseq____&quot;,226,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^Hlogseq____&quot;,229,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^Hlogseq____&quot;,230,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^Hlogseq____&quot;,236,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^Hlogseq____&quot;,237,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^17logseq____&quot;,true,536870940]],[logseq____&quot;^15logseq____&quot;,[480,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-155c-413d-9082-2b142a404472logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[481,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Nach Ersetzung von $x$ in der AF $\\logseq____&quot;xlogseq____&lt;y\\logseq____&quot;$ durch eine konkrete Zahl entsteht eine AF in der Variablen $y$, z. Bsp. $\\logseq____&quot;17logseq____&lt;y\\logseq____&quot;$logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[481,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[481,logseq____&quot;^Flogseq____&quot;,468,536870940]],[logseq____&quot;^15logseq____&quot;,[481,logseq____&quot;^Xlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[481,logseq____&quot;^Vlogseq____&quot;,468,536870940]],[logseq____&quot;^15logseq____&quot;,[481,logseq____&quot;^Ulogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[481,logseq____&quot;^Ulogseq____&quot;,238,536870940]],[logseq____&quot;^15logseq____&quot;,[481,logseq____&quot;^17logseq____&quot;,true,536870940]],[logseq____&quot;^15logseq____&quot;,[481,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-c95b-4009-af2e-2994c853a49alogseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[482,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\forall x:p(x)$ ist die [Aussage]([[Aussagen]]): $\\logseq____&quot;\\\\text{Für alle x aus U ist p(x) wahr}\\logseq____&quot;\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w\\\\quadlogseq____&amp;\\\\text{fallls p(x) w für alle x aus U}\\\\\\\\f\\\\quadlogseq____&amp;\\\\text{falls p(x) f für (wenigstens) ein x aus 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beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der [[Aussagenlogik]]logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[485,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[485,logseq____&quot;^Flogseq____&quot;,503,536870940]],[logseq____&quot;^15logseq____&quot;,[485,logseq____&quot;^Xlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[485,logseq____&quot;^Vlogseq____&quot;,478,536870940]],[logseq____&quot;^15logseq____&quot;,[485,logseq____&quot;^Ulogseq____&quot;,224,536870940]],[logseq____&quot;^15logseq____&quot;,[485,logseq____&quot;^Ulogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[485,logseq____&quot;^Ulogseq____&quot;,238,536870940]],[logseq____&quot;^15logseq____&quot;,[485,logseq____&quot;^Ulogseq____&quot;,243,536870940]],[logseq____&quot;^15logseq____&quot;,[485,logseq____&quot;^Hlogseq____&quot;,224,536870940]],[logseq____&quot;^15logseq____&quot;,[485,logseq____&quot;^Hlogseq____&quot;,243,536870940]],[logseq____&quot;^15logseq____&quot;,[485,logseq____&quot;^17logseq____&quot;,true,536870940]],[logseq____&quot;^15logseq____&quot;,[485,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-74fb-465b-a06d-feffcb800367logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[486,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[486,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[486,logseq____&quot;^Flogseq____&quot;,472,536870940]],[logseq____&quot;^15logseq____&quot;,[486,logseq____&quot;^Xlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[486,logseq____&quot;^Vlogseq____&quot;,474,536870940]],[logseq____&quot;^15logseq____&quot;,[486,logseq____&quot;^Ulogseq____&quot;,39,536870940]],[logseq____&quot;^15logseq____&quot;,[486,logseq____&quot;^Ulogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[486,logseq____&quot;^Ulogseq____&quot;,228,536870940]],[logseq____&quot;^15logseq____&quot;,[486,logseq____&quot;^Ulogseq____&quot;,232,536870940]],[logseq____&quot;^15logseq____&quot;,[486,logseq____&quot;^Ulogseq____&quot;,238,536870940]],[logseq____&quot;^15logseq____&quot;,[486,logseq____&quot;^Hlogseq____&quot;,39,536870940]],[logseq____&quot;^15logseq____&quot;,[486,logseq____&quot;^17logseq____&quot;,true,536870940]],[logseq____&quot;^15logseq____&quot;,[486,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fddf5-7b87-4c87-b597-13b1e7d30085logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[487,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Allquantor]] 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x: p(x) logseq____&amp;\\\\equiv p(O_1) \\\\land p(O_2) \\\\land \\\\cdots \\\\land p(O_m)\\\\\\\\\\n\\\\underbrace{\\\\exists}_\\\\text{Existenzquantor} x: p(x) logseq____&amp;\\\\equiv p(0_1) \\\\lor p(O_2) \\\\lor \\\\cdots \\\\lor 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[[Regeln]]logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[489,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870940]],[logseq____&quot;^15logseq____&quot;,[489,logseq____&quot;^Flogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[489,logseq____&quot;^Xlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[489,logseq____&quot;^Vlogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[489,logseq____&quot;^Ulogseq____&quot;,220,536870940]],[logseq____&quot;^15logseq____&quot;,[489,logseq____&quot;^Ulogseq____&quot;,227,536870940]],[logseq____&quot;^15logseq____&quot;,[489,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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= Beweisende, auch [q.e.d.]([[Q.E.D.]]), [[w.z.b.w.]], QED, 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x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist 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[[Quantoren]] dürfen **nicht** vertauscht 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(AF) über [Universen]([[Universen (Logik)]]) 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[[Potenzen]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Flogseq____&quot;,96,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Potenzen]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Flogseq____&quot;,59,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Vlogseq____&quot;,59,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Hlogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-91dc-4973-a77e-cd75b12e5244logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;https://www.wolframalpha.comlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Flogseq____&quot;,66,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Vlogseq____&quot;,66,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,44,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,46,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-9411-4aa9-8b0f-8632bb2dd466logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])\\n\\\\begin{align}\\nx^4-34x^2+225logseq____&amp;=0\\\\\\\\\\n\\\\text{substituiert }ylogseq____&amp;=x^2\\\\\\\\\\ny^2-34y+225logseq____&amp;=0\\\\\\\\\\ny_{1,2}logseq____&amp;=17\\\\pm\\\\sqrt{(-17)^2-225}\\\\\\\\\\nlogseq____&amp;=17\\\\pm\\\\sqrt{289-225}\\nlogseq____&amp;=17\\\\pm\\\\sqrt{64}=17\\\\pm8\\\\\\\\\\nlogseq____&amp;=\\\\left.\\\\begin{cases}\\n25\\\\\\\\\\n9\\n\\\\end{cases}\\\\right|\\\\begin{array}{l}\\nx^2=25logseq____&amp;\\\\rightarrow logseq____&amp;x_1=5;logseq____&amp;x_2=-5\\\\\\\\\\nx^2=9logseq____&amp;\\\\rightarrow logseq____&amp;x_1=3;logseq____&amp;x_2=-3\\\\\\\\\\n\\\\end{array}\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Flogseq____&quot;,58,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Vlogseq____&quot;,56,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Hlogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d7-9d19-41e1-80fd-6ba23228c4b2logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn } 10^x=y \\\\text{, dann}$\\n\\\\begin{align}\\nxlogseq____&amp;=\\\\lg y logseq____&amp; ,r\\\\\\\\\\nxlogseq____&amp;=\\\\log_y10logseq____&amp;,f\\\\\\\\\\nxlogseq____&amp;=\\\\log_{10}ylogseq____&amp;,r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&amp;= \\\\ln 2 logseq____&amp;, r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&amp;= \\\\ln 8 logseq____&amp;, f \\\\\\\\\\n\\\\ln 4 + \\\\ln 2 logseq____&amp;= \\\\ln 8 logseq____&amp;, r \\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Flogseq____&quot;,102,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Vlogseq____&quot;,102,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,31,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-2f5d-4cd0-92bc-fcf4d0504c18logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Wurzeln]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Flogseq____&quot;,61,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Vlogseq____&quot;,59,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Hlogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-3223-4c3c-9c09-063fb81890f8logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wolframalpha]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Flogseq____&quot;,96,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Vlogseq____&quot;,96,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,44,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,46,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Hlogseq____&quot;,46,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-9892-44a7-9de1-ba261a59b929logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Wenn }alogseq____&gt;0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac b{\\\\sqrt a} = \\\\frac b{\\\\sqrt a}*\\\\frac{\\\\sqrt a}{\\\\sqrt a} = \\\\frac {b\\\\sqrt a}a\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Flogseq____&quot;,47,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Vlogseq____&quot;,47,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Ulogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d7-218b-4a5a-a813-ded68cacc9b9logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Wurzeln]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Flogseq____&quot;,102,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Hlogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-a1ba-465a-b8fa-e89642aba357logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Häufige Falle:}$\\n\\\\begin{align}\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&amp;=(-1)^\\\\frac22logseq____&amp;=(-1)^1logseq____&amp;=-1\\\\\\\\\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&amp;=1^\\\\frac12logseq____&amp;logseq____&amp;=1\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Flogseq____&quot;,77,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Vlogseq____&quot;,68,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-ac6b-4c8a-91c0-5789047dac2clogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Allgemein}$\\n\\\\begin{align}\\n|y|logseq____&amp;=\\\\begin{cases}\\ny logseq____&amp;\\\\text{ falls } y\\\\ge0\\\\\\\\\\n-y logseq____&amp;\\\\text{ falls } ylogseq____&lt;0\\\\\\\\\\n\\\\end{cases}\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Flogseq____&quot;,50,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Vlogseq____&quot;,65,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-af2c-45f8-aa27-4e70c52922d6logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Für } x=\\\\frac25 \\\\text{ und } y=\\\\frac37 \\\\text{ ist }\\\\frac xy$\\n\\\\begin{align}\\n\\\\frac xy = \\\\frac{\\\\frac25}{\\\\frac37} = \\\\frac{2*7}{3*5}=\\\\frac{14}{15}\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Flogseq____&quot;,103,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Vlogseq____&quot;,103,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-13d1-4a3c-b0eb-426396245365logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Binomische Formeln]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Flogseq____&quot;,89,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Hlogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-28a7-45bd-a80f-c412fd3cc6calogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Flogseq____&quot;,81,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Vlogseq____&quot;,81,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Hlogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-349c-4740-b1b3-eef2d7f3db9elogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche quadratische Gleichung hat die Lösung}$\\n$x_1=3\\\\quad x_2=4$\\n\\\\begin{align}\\nx_1+x_2 = 7 logseq____&amp;= p logseq____&amp;, x_1x_2=12=q\\\\\\\\\\nx^2+px+qlogseq____&amp;=0\\\\\\\\\\nx^2-7x+12logseq____&amp;=0\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Flogseq____&quot;,94,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Vlogseq____&quot;,94,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d7-e067-4e5a-b1ef-f7cfca8a3e83logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Alte Schreibweise}$\\n\\\\begin{align}\\n\\\\text{cosa }logseq____&amp;\\\\text{plus }logseq____&amp;\\\\text{cubus }logseq____&amp;\\\\text{acq }logseq____&amp;6\\\\\\\\\\nxlogseq____&amp;+logseq____&amp;x^3logseq____&amp;=logseq____&amp;6\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Flogseq____&quot;,79,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Vlogseq____&quot;,61,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-eeae-4fc1-8bae-d1da0caeeb86logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Wurzelgleichung]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Flogseq____&quot;,104,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Vlogseq____&quot;,59,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,30,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Hlogseq____&quot;,30,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d7-e3bb-4cfc-9cc6-b1776ba94a3elogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn }alogseq____&gt;0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=a\\\\sqrt{a}logseq____&amp;,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=a^2-\\\\sqrt{a}logseq____&amp;,f\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=\\\\sqrt{a^3}logseq____&amp;,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=a^{\\\\frac32}logseq____&amp;,r\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Flogseq____&quot;,68,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Vlogseq____&quot;,68,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-fcc4-428b-9e7a-72db00d65bfflogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Flogseq____&quot;,90,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Vlogseq____&quot;,86,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Hlogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-4c60-4f70-935a-0f3fa4faa2d3logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Flogseq____&quot;,84,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Vlogseq____&quot;,61,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Hlogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-7300-4505-99f4-300a51856c4flogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Einsetzen, um zu überprüfen, ob man eine Fallunterscheidung brauchtlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Flogseq____&quot;,52,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Vlogseq____&quot;,76,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ulogseq____&quot;,30,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d7-05e6-4275-bb58-c717ca74da94logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\n\\\\tan x logseq____&amp;= \\\\frac{\\\\sin x}{\\\\cos x} logseq____&amp;, \\\\cos x \\\\ne 0\\\\\\\\\\n\\\\sin^{-2}x-\\\\cos^2xlogseq____&amp;=1logseq____&amp;,f\\\\\\\\\\n\\\\sin x = \\\\cos x logseq____&amp;= 1 logseq____&amp;, f\\\\\\\\\\n\\\\sin^{-2}x+cos^2ylogseq____&amp;=1logseq____&amp;,r\\\\\\\\\\n1+tan^2xlogseq____&amp;=\\\\frac1{\\\\cos^2x}logseq____&amp;,\\\\cos x\\\\ne0\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Flogseq____&quot;,49,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Vlogseq____&quot;,89,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-45c5-423f-8bf5-cd7cc59f46a4logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel für die 3. Binomische Formel}$\\n\\\\begin{align}\\n\\\\frac{\\\\frac1{a-b}+\\\\frac1{a+b}}{\\\\frac1{a-b}-\\\\frac1{a+b}}\\nlogseq____&amp;=\\\\frac{\\\\frac{a+b+a-b}{(a+b)*(a-b)}}{\\\\frac{a+b-(a-b)}{(a+b)*(a-b)}}\\nlogseq____&amp;=\\\\frac{a+b+a-b}{a+b-a+b}\\nlogseq____&amp;=\\\\frac{2a}{2b}\\nlogseq____&amp;=\\\\frac ab\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Flogseq____&quot;,51,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Vlogseq____&quot;,72,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-4ae0-44da-abe0-456f9ef2d3c3logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\underbrace{\\\\frac6{2+\\\\sqrt2}*\\\\frac{2-\\\\sqrt2}{2-\\\\sqrt2}\\n= \\\\frac{6(2-\\\\sqrt2)}{2^2-(\\\\sqrt2)^2}}_\\\\text{3. binomische Formel}\\nlogseq____&amp;=\\\\frac{6(2-\\\\sqrt2)}2=3(2-\\\\sqrt2)\\\\\\\\\\n\\\\frac{a-b}{\\\\sqrt a+\\\\sqrt b}logseq____&amp;=\\\\frac{a-b}{\\\\sqrt a + \\\\sqrt b}\\\\frac{\\\\sqrt a-\\\\sqrt b}{\\\\sqrt a-\\\\sqrt b}logseq____&amp;, a,b,logseq____&gt;0\\\\notag\\\\\\\\\\n=\\\\frac{(a-b)(\\\\sqrt a-\\\\sqrt b)}{(a-b)}logseq____&amp;=\\\\sqrt a\\\\sqrt b\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Flogseq____&quot;,91,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Vlogseq____&quot;,91,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d7-af72-4044-833e-20615ddf257elogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\na^nlogseq____&amp;=\\\\underbrace{a*a*\\\\cdots*n}_n logseq____&amp; a,blogseq____&gt;0\\\\\\\\\\na^2b^2logseq____&amp;=(ab)^n\\\\\\\\\\n\\\\frac{a^n}{b^n}logseq____&amp;=\\\\left(\\\\frac ab\\\\right)^n\\\\\\\\\\na^na^mlogseq____&amp;=a^{n+m}\\\\\\\\\\n\\\\frac1{a^n}logseq____&amp;=a^{-n}\\\\\\\\\\n(a^n)^mlogseq____&amp;=a^{nm}\\\\\\\\\\na^0logseq____&amp;=1\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Flogseq____&quot;,61,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Vlogseq____&quot;,61,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-e5ab-4085-a527-0bbe9e728caflogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Die Lösung von } x^n-a=0 \\\\text{ ist } x=\\\\sqrt[n]a$ #FIXME ich glaube hier fehlt logseq____&gt;0 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[[Pascalsches Dreieck]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Flogseq____&quot;,82,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Vlogseq____&quot;,72,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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von [Punkten]([[Punkte]]) $(x,y)$ in der [Ebene]([[Ebenen]])  die den gleichen [[Abstand]] r ([[Radius]]) zu einem festen [Punkt]([[Punkte]]) 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*(-1)\\\\\\\\\\nxlogseq____&amp;logseq____&gt;11\\n\\\\end{align}\\n\\\\begin{align}\\nL_3=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|xlogseq____&gt;3,xlogseq____&gt;11\\\\right\\\\}=(11,\\\\infty)\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Flogseq____&quot;,137,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Xlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Vlogseq____&quot;,140,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Ulogseq____&quot;,108,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Ulogseq____&quot;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Ulogseq____&quot;,118,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-8207-4c8d-9295-81c50ebdef1flogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Flogseq____&quot;,128,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Xlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Vlogseq____&quot;,128,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Ulogseq____&quot;,108,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Ulogseq____&quot;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Ulogseq____&quot;,118,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Jlogseq____&quot;,[],536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Hlogseq____&quot;,108,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-589b-421e-85d8-193571fe41dclogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 2b}\\\\quad xlogseq____&lt;-2$\\n\\\\begin{align}\\n|\\\\underbrace{x+2}_{logseq____&lt;0}logseq____&amp;=-(x+2)=-x-2\\\\\\\\\\n-x+3logseq____&amp;\\\\le -x-2 logseq____&amp;|logseq____&amp;+x\\\\\\\\\\n3logseq____&amp;\\\\le-2logseq____&amp;logseq____&amp;\\\\underset{falsche Aussage}{f.A}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Flogseq____&quot;,156,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Xlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Vlogseq____&quot;,142,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Ulogseq____&quot;,108,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Ulogseq____&quot;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Ulogseq____&quot;,118,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-4aa1-40ce-982d-665bc0fad071logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Flogseq____&quot;,162,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Xlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Vlogseq____&quot;,162,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Ulogseq____&quot;,108,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Ulogseq____&quot;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Ulogseq____&quot;,118,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Jlogseq____&quot;,[],536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Hlogseq____&quot;,108,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-641b-4cd2-90dc-c30c57d14cealogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;![draws/2023-10-13-18-01-25.excalidraw](https://raw.githubusercontent.com/Surferlul/IA-Logseq-Publish/external-assets/svg-assets/draws/2023-10-13-18-01-25.excalidraw.svg)logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Flogseq____&quot;,148,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Xlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Vlogseq____&quot;,157,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Ulogseq____&quot;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Ulogseq____&quot;,118,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-3ac7-4399-b5d2-7ef8b2897311logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 2}\\\\quad xlogseq____&lt;3$\\n\\\\begin{align}\\n|\\\\underbrace{x-3}_{logseq____&lt;0}|logseq____&amp;=6(x-3)=-x+3\\\\\\\\\\n-x+3logseq____&amp;\\\\le|x+2|\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Flogseq____&quot;,151,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Xlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Vlogseq____&quot;,142,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Ulogseq____&quot;,108,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Ulogseq____&quot;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Ulogseq____&quot;,118,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-fe41-4a7b-ac65-2fcf94f5ec4flogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[145,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nM=\\\\left\\\\{\\\\underbrace{(x,y)}_\\\\text{Punkte der Ebene}\\\\in\\\\Reals^2\\\\middle|y=|x|\\\\right\\\\}\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[145,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[145,logseq____&quot;^Flogseq____&quot;,143,536870920]],[logseq____&quot;^15logseq____&quot;,[145,logseq____&quot;^Xlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[145,logseq____&quot;^Vlogseq____&quot;,143,536870920]],[logseq____&quot;^15logseq____&quot;,[145,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[145,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[145,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[145,logseq____&quot;^Ulogseq____&quot;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[145,logseq____&quot;^Ulogseq____&quot;,118,536870920]],[logseq____&quot;^15logseq____&quot;,[145,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[145,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-3157-49cf-bc4e-319594e6a422logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^Flogseq____&quot;,147,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^Xlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^Vlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-c79b-4bd2-8403-364ad37d9811logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME incompletelogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Flogseq____&quot;,153,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Xlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Vlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Ulogseq____&quot;,42,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Hlogseq____&quot;,42,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-ea6c-4143-acbe-d411704eda39logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[148,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;![draws/2023-10-13-17-57-31.excalidraw](https://raw.githubusercontent.com/Surferlul/IA-Logseq-Publish/external-assets/svg-assets/draws/2023-10-13-17-57-31.excalidraw.svg)logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[148,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[148,logseq____&quot;^Flogseq____&quot;,157,536870920]],[logseq____&quot;^15logseq____&quot;,[148,logseq____&quot;^Xlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[148,logseq____&quot;^Vlogseq____&quot;,157,536870920]],[logseq____&quot;^15logseq____&quot;,[148,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[148,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[148,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[148,logseq____&quot;^Ulogseq____&quot;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[148,logseq____&quot;^Ulogseq____&quot;,118,536870920]],[logseq____&quot;^15logseq____&quot;,[148,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[148,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-6d50-4d25-a218-74565650d9fdlogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 1}\\\\quad x\\\\ge3$\\n\\\\begin{align}\\n|x-3|logseq____&amp;=x-3\\\\\\\\\\nx-3\\\\le|x+2|\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Flogseq____&quot;,142,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Xlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Vlogseq____&quot;,142,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Ulogseq____&quot;,108,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Ulogseq____&quot;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Ulogseq____&quot;,118,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-8a87-428d-b488-c10776712710logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Betragsungleichungen]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Flogseq____&quot;,132,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Xlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Vlogseq____&quot;,131,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Ulogseq____&quot;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Ulogseq____&quot;,118,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Jlogseq____&quot;,[],536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Hlogseq____&quot;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-f9dd-46df-81f8-8e26141f05b4logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 1b}\\\\quad xlogseq____&lt;-2\\\\quad\\\\text{Wiederspricht Bedingung}\\\\quad x\\\\ge3$logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Flogseq____&quot;,158,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Xlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Vlogseq____&quot;,142,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Ulogseq____&quot;,108,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Ulogseq____&quot;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Ulogseq____&quot;,118,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-097b-45b8-9ccc-a5e142b096falogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Flogseq____&quot;,122,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Xlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Vlogseq____&quot;,150,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Ulogseq____&quot;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Ulogseq____&quot;,118,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Hlogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-8aab-4348-b9bb-047d104d7ab3logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Mengen]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Flogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Xlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Vlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Ulogseq____&quot;,118,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Jlogseq____&quot;,[],536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Hlogseq____&quot;,118,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^17logseq____&quot;,false,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-2a70-49a1-a943-b725eb6645d8logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[154,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[154,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[154,logseq____&quot;^Flogseq____&quot;,126,536870920]],[logseq____&quot;^15logseq____&quot;,[154,logseq____&quot;^Xlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[154,logseq____&quot;^Vlogseq____&quot;,126,536870920]],[logseq____&quot;^15logseq____&quot;,[154,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[154,logseq____&quot;^Ulogseq____&quot;,108,536870920]],[logseq____&quot;^15logseq____&quot;,[154,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[154,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[154,logseq____&quot;^Ulogseq____&quot;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[154,logseq____&quot;^Ulogseq____&quot;,118,536870920]],[logseq____&quot;^15logseq____&quot;,[154,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870920]],[logseq____&quot;^15logseq____&quot;,[154,logseq____&quot;^Jlogseq____&quot;,[],536870920]],[logseq____&quot;^15logseq____&quot;,[154,logseq____&quot;^Hlogseq____&quot;,108,536870920]],[logseq____&quot;^15logseq____&quot;,[154,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[154,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-42be-46f6-855f-1cd904fb2533logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[155,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Beispiele]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[155,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[155,logseq____&quot;^Flogseq____&quot;,125,536870920]],[logseq____&quot;^15logseq____&quot;,[155,logseq____&quot;^Xlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[155,logseq____&quot;^Vlogseq____&quot;,153,536870920]],[logseq____&quot;^15logseq____&quot;,[155,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[155,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[155,logseq____&quot;^Ulogseq____&quot;,118,536870920]],[logseq____&quot;^15logseq____&quot;,[155,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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$\\\\rightarrow$ 5 ist abstand von x zu 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logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870920]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Jlogseq____&quot;,[],536870920]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Hlogseq____&quot;,106,536870920]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-1a3f-40f3-a01f-2f6769b82b8blogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 2}\\\\quad x\\\\ge3$\\n\\\\begin{align}\\n|x-3|logseq____&amp;=-x+3\\\\\\\\\\nx-3logseq____&amp;logseq____&lt;5 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Meinel, M. Mundhenk,  [[\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. Auflage 2011]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Flogseq____&quot;,195,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Vlogseq____&quot;,195,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Hlogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-9931-42a0-b034-0ca1f38ecb3alogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Soweit die \\logseq____&quot;[[Syntax]]\\logseq____&quot;, jetzt die [[Semantik]]. Die [Wahrheitswerte]([[Wahrheitswert]])\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Flogseq____&quot;,191,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Vlogseq____&quot;,214,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,172,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,177,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,179,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,183,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Hlogseq____&quot;,172,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Hlogseq____&quot;,177,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Hlogseq____&quot;,179,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Hlogseq____&quot;,183,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-3171-456a-a4d2-78c47082e179logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Büchertiplogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Flogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Vlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^17logseq____&quot;,false,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-8f0b-4ef0-b71b-eff0bb1e5f9elogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Weitere [[Beispiele]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Flogseq____&quot;,198,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Vlogseq____&quot;,214,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Hlogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-4fcb-4a45-835d-3e78bb50883elogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\nlogseq____&amp;\\logseq____&quot;5\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;\\\\quadlogseq____&amp; (w)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;4\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;logseq____&amp; (f)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Jede gerade Zahl }\\\\ge4\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ ist Summe zweier Primzahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage, }w\\\\text{ oder }f)\\\\notag\\\\\\\\\\nlogseq____&amp;(\\\\text{Vermutung von Goldback 1742})\\\\text{, }logseq____&amp;logseq____&amp;\\\\text{richtig für gerade Zahlen bis }4*10^{18}\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Dieser Satz ist falsch}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{keine Aussage})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Gleichung } x^2+y^2=z^2 \\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ hat eine Lösung }x,y,z\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nlogseq____&amp;x^n+y^n=z^n\\\\text{ eine Lösung}logseq____&amp;logseq____&amp; (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nlogseq____&amp;x,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp;\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Gott ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Nietzsche ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Flogseq____&quot;,203,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Vlogseq____&quot;,207,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-019c-42a5-be2d-c9425e24188elogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Flogseq____&quot;,210,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Vlogseq____&quot;,214,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Hlogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-393f-4153-a862-cc1f9e57b863logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $f$ istlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Flogseq____&quot;,189,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Vlogseq____&quot;,189,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,175,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-e399-4712-881b-96222b7679aflogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sind $p$ und $q$ [[Aussagen]], so auch\\n\\\\begin{align}\\n(p\\\\land q) logseq____&amp;\\\\quadlogseq____&amp; (\\logseq____&quot;\\\\text{und}\\logseq____&quot;)\\\\\\\\\\n(p\\\\lor q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{oder}\\logseq____&quot;)\\\\\\\\\\n(\\\\neg p) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{nicht}\\logseq____&quot;)\\\\\\\\\\n(p\\\\rightarrow q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{impliziert}\\logseq____&quot;)\\\\\\\\\\n(p\\\\leftrightarrow q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{genau dann wenn}\\logseq____&quot;)\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Flogseq____&quot;,214,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Vlogseq____&quot;,214,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Hlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-6d63-41f1-9447-4705c20f7c1blogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $w$ istlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Flogseq____&quot;,213,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Vlogseq____&quot;,213,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-bc05-4e45-b3d2-f57cdcdbfe55logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\np\\\\land q\\\\lor r\\\\\\\\\\n(p\\\\land q)\\\\lor r\\\\\\\\\\np\\\\land (q\\\\lor r)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Flogseq____&quot;,191,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Vlogseq____&quot;,191,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-0bf7-4f84-9a8c-1e4f3a5e02e1logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Satz, der wahr oder falsch ist, d.h. der [[Wahrheitswert]] $w$ bzw $f$ hat ($t/f$, $1/0$, $\\\\text{wahr}/\\\\text{falsch}$)logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Flogseq____&quot;,207,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Vlogseq____&quot;,207,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,172,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Hlogseq____&quot;,172,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-e85b-4e77-b8a8-5e260bc41698logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Flogseq____&quot;,212,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Vlogseq____&quot;,214,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Hlogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Hlogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-c342-4ed4-b195-b8a551170469logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Zuordnung von $w/f$ an jede [Variable]([[Variablen]]) einer [[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Flogseq____&quot;,212,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Vlogseq____&quot;,212,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,186,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Hlogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Hlogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-d89a-4baf-8d06-cfcb742e3769logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel: Bestimmung des }$[[Wahrheitswerteverlauf]]$\\\\text{ von }(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)$\\n|$p$|$q$||$p\\\\rightarrow q$|$q\\\\rightarrow p$|$(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)|$p\\\\leftrightarrow q$|\\n|-|-|-|-|-|-|\\n|f|f||w|w|w|w|\\n|f|w||w|f|f|f|\\n|w|f||f|w|f|f|\\n|w|w||w|w|w|w|logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Flogseq____&quot;,211,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Vlogseq____&quot;,204,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Hlogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-1e63-468e-904d-51f4f09136f2logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 1. [[Aussagen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Flogseq____&quot;,195,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Vlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Hlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-5f98-4d25-99c5-fcf4636975c3logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Flogseq____&quot;,187,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Vlogseq____&quot;,187,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,42,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,181,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Hlogseq____&quot;,42,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Hlogseq____&quot;,181,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-6fb9-4eeb-b64a-48ef7cae4d24logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Variable]([[Variablen]]), die den Wert $w$ oder $f$ annimmtlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Flogseq____&quot;,190,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Vlogseq____&quot;,190,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ulogseq____&quot;,169,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ulogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Hlogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-6b5e-40ac-99dd-c0b6c2f17c0flogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formeln $p,q$ [logisch äquivalent]([[Logisch Äquivalent]]), wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Flogseq____&quot;,189,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Vlogseq____&quot;,214,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,185,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Hlogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Hlogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Hlogseq____&quot;,185,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-f8a6-4e3b-9f00-b2fff017ef02logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Flogseq____&quot;,204,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Vlogseq____&quot;,204,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,171,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,172,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,179,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,186,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Hlogseq____&quot;,171,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Hlogseq____&quot;,172,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Hlogseq____&quot;,179,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Hlogseq____&quot;,186,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-d5d5-4d1b-9588-b9e749a6c4b0logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Belegung]] (der [[Variablen]])logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Flogseq____&quot;,187,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Vlogseq____&quot;,214,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,186,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Hlogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Hlogseq____&quot;,186,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-e28a-490b-befa-a717b6be1703logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Tantologie]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Flogseq____&quot;,204,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Vlogseq____&quot;,214,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ulogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Hlogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-f1a6-4880-8adb-2dd6e703bc83logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Verknüpfung von Aussagen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Flogseq____&quot;,197,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Xlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Vlogseq____&quot;,207,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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morgansche regelnlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^11logseq____&quot;,logseq____&quot;de Morgansche 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U}\\\\end{cases}$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Flogseq____&quot;,258,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,172,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Hlogseq____&quot;,172,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-1617-4a16-8155-212a65cbcf39logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;wobei $\\\\pi$ eine \\logseq____&quot;[[Permutation]]\\logseq____&quot; der Zahl $(1,2,\\\\cdots,n)$ istlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Flogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Vlogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,230,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Hlogseq____&quot;,230,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-fc44-421d-8b0a-a34bc07ad536logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist wahr}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Flogseq____&quot;,271,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Vlogseq____&quot;,271,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Hlogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-1647-46e0-a2e6-e169ce0b3f73logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Widerspruch = ↯, #logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Flogseq____&quot;,266,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Vlogseq____&quot;,266,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-f5ff-48be-be19-f26027972a14logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Flogseq____&quot;,250,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Vlogseq____&quot;,250,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,219,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,231,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,236,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Hlogseq____&quot;,219,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Hlogseq____&quot;,231,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Hlogseq____&quot;,236,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-8d8e-4613-87b9-66e20ba220d1logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Regeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Flogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Vlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Hlogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^17logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-e1bd-400a-af99-8c4d193ffabflogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x,y)$ AF in Variablen $x,y$ über $U_1,U_2$\\n\\\\begin{align}\\n\\\\underbrace{\\\\forall x: \\\\underbrace{\\\\exists y: p(x,y)}_{\\\\text{AF in den Variablen }x\\\\text{ über }U_1}}_{\\\\text{Aussage}}\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Flogseq____&quot;,264,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Vlogseq____&quot;,264,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-c39e-4e9d-809c-80cebb41d7a2logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Nach Ersetzung von $x$ in der AF $\\logseq____&quot;xlogseq____&lt;y\\logseq____&quot;$ durch eine konkrete Zahl entsteht eine AF in der Variablen $y$, z. Bsp. $\\logseq____&quot;17logseq____&lt;y\\logseq____&quot;$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Flogseq____&quot;,274,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Vlogseq____&quot;,274,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-b54c-4676-b00d-27aaebad1bf9logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nlogseq____&amp;\\\\forall x: \\\\forall y: p(x, y) \\\\equiv \\\\forall y: \\\\forall x: p(x,y)\\\\\\\\\\nlogseq____&amp;\\\\exists x:\\\\exists y:p(x,y)\\\\equiv\\\\exists y:\\\\exists x:p(x,y)\\\\\\\\\\nlogseq____&amp;[\\\\forall x_1:\\\\forall x_2: \\\\cdots:\\\\forall x_n:p(x_1,x_2,\\\\cdots,x_n)\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\equiv\\\\forall_{x_{\\\\pi(1)}}:\\\\forall_{x_{\\\\pi(1)}}:\\\\cdots:\\\\forall_{x_{\\\\pi(1)}}:p(x_1,x_2,\\\\cdots,x_n)\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Flogseq____&quot;,256,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Vlogseq____&quot;,256,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-43b0-4143-96ef-c99f45f3e453logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:(p(x)\\\\land q(x)) logseq____&amp;\\\\equiv (\\\\forall x: p(x)) \\\\land (\\\\forall x:q(x));\\\\notag\\\\\\\\\\n\\\\exists x: (p(x) \\\\lor q(x)) logseq____&amp;\\\\equiv (\\\\exists x: p(x))\\\\lor(\\\\exists x: q(x)),\\\\quadlogseq____&amp;\\\\text{Große Assoziativgesetze}\\\\\\\\\\n\\\\neg(\\\\forall x:p(x))logseq____&amp;\\\\equiv \\\\exists x: (\\\\neg p(x));\\\\quadlogseq____&amp;\\\\text{Große de Morgansche Regeln;}\\\\notag\\\\\\\\\\n\\\\neg(\\\\exists x: p(x)) logseq____&amp;\\\\equiv \\\\forall x: (\\\\neg p(x)),\\\\quadlogseq____&amp;\\\\text{Negationsregeln.}\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Flogseq____&quot;,277,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Vlogseq____&quot;,277,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-e0a2-4733-afe2-c64525a0bfe3logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativschreibweisen:\\n$\\\\forall x: p(x)$ auch $\\\\bigwedge x:p(x)$\\n$\\\\exists x:p(x)$ auch $\\\\bigvee x:p(x)$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Flogseq____&quot;,241,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-fc8e-4d63-b48f-b4b0556b6ca7logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Flogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Vlogseq____&quot;,256,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Hlogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-64f5-4e6e-87e5-0fc74b697f77logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXMElogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Flogseq____&quot;,251,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Vlogseq____&quot;,251,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,42,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Hlogseq____&quot;,42,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-5851-4f5b-90f2-08bcef64eddelogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nlogseq____&amp;\\\\neg\\\\left(\\\\forall x :\\\\exists y :\\\\forall w :\\\\forall u :\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)\\\\right)\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x:(\\\\neg(\\\\exists y: \\\\forall w: \\\\forall u: \\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x:\\\\forall y:(\\\\neg(\\\\forall w: \\\\forall u:\\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x:\\\\forall y:\\\\exists w:(\\\\neg(\\\\forall u:\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x: \\\\forall y: \\\\exists w: \\\\exists u : \\\\forall z:\\\\neg(p(x,y,z)\\\\rightarrow q(u,w))\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Flogseq____&quot;,273,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Vlogseq____&quot;,273,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-b87c-4651-b28d-f491ae06c054logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Für das leere Universum gilt\\n\\\\begin{align}\\n\\\\forall x: p(x)\\\\quadlogseq____&amp;Tautologie\\\\\\\\\\n\\\\exists x: p(x)\\\\quadlogseq____&amp;Kontradiktion\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Flogseq____&quot;,269,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-aab4-495e-b9d7-c97ce8c2cea6logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Gleichartige]([[Gleichartig]]) [[Quantoren]] dürfen vertauscht werdenlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Flogseq____&quot;,277,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Hlogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Hlogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-7a6e-4357-aa04-9d206bdca0d7logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $x$ aus $\\\\Reals$ beliebig. Setze $y:=x+1$ (ist aus $\\\\Reals$). Dann ist $xlogseq____&lt;x+1=y$ also $xlogseq____&lt;y$. $\\\\blacksquare$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Flogseq____&quot;,243,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Vlogseq____&quot;,243,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-416c-45b7-b321-82b02f61da10logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\underbrace{\\\\forall}_\\\\text{Allquantor} x: p(x) logseq____&amp;\\\\equiv p(O_1) \\\\land p(O_2) \\\\land \\\\cdots \\\\land p(O_m)\\\\\\\\\\n\\\\underbrace{\\\\exists}_\\\\text{Existenzquantor} x: p(x) logseq____&amp;\\\\equiv p(0_1) \\\\lor p(O_2) \\\\lor \\\\cdots \\\\lor p(0_m)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Flogseq____&quot;,278,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-3738-4520-b398-d8f4017cb774logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\forall x:p(x)$ ist die [Aussage]([[Aussagen]]): $\\logseq____&quot;\\\\text{Für alle x aus U ist p(x) wahr}\\logseq____&quot;\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w\\\\quadlogseq____&amp;\\\\text{fallls p(x) w für alle x aus U}\\\\\\\\f\\\\quadlogseq____&amp;\\\\text{falls p(x) f für (wenigstens) ein x aus U}\\\\end{cases}$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Flogseq____&quot;,272,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Vlogseq____&quot;,272,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,172,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,180,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Hlogseq____&quot;,172,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Hlogseq____&quot;,180,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-f4a6-4c93-8689-22ebabcb33belogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Allquantor]] [[Existenzquantor]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Flogseq____&quot;,258,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Vlogseq____&quot;,258,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Hlogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Hlogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-64ab-4bda-af35-c90166e77774logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist falsch}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Flogseq____&quot;,243,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Vlogseq____&quot;,271,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Hlogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-d439-4a7c-b5f5-10f78d695ef6logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Verschiedene [[Quantoren]] dürfen **nicht** vertauscht werdenlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Flogseq____&quot;,242,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Vlogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Hlogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-cdfa-4fe0-9de1-4f76d182733dlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Flogseq____&quot;,268,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Hlogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-ba1c-440e-b74d-274f9e49c0f4logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Schachtelung von quantoren ([Beispiel]([[Beispiele]])):logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Flogseq____&quot;,250,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Vlogseq____&quot;,277,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Hlogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-ae9a-40eb-9e17-91492d005467logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Aussageform]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Flogseq____&quot;,270,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Vlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Hlogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-4b2f-4784-80e6-af2c8bbc2b8blogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Wäre $y$ aus $\\\\Reals$ mit $xlogseq____&lt;y$ für alle $x$ aus $\\\\Reals$, so insbesondere auch $ylogseq____&lt;y$, Widerspruch. $\\\\blacksquare$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Flogseq____&quot;,261,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Vlogseq____&quot;,261,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-140c-44d1-8b35-9a4bdc6ad503logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Aussageform]] (AF) über [Universen]([[Universen (Logik)]]) $U_1,\\\\cdots,U_n$:logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Flogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,238,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Hlogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Hlogseq____&quot;,238,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-1f8b-47ba-96c8-ea4fa014161elogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Satz]] mit [[Variablen]] $x_1,\\\\cdots,x_n$, der bei Ersetzung jedes $x_j$ durch ein [Objekt]([[Objekt (Logik)]]) aus $U_j$ stets zu einer [Aussage]([[Aussagen]]) wirdlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Flogseq____&quot;,267,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,176,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,180,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,240,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Hlogseq____&quot;,176,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Hlogseq____&quot;,180,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Hlogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Hlogseq____&quot;,240,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-d5cf-448f-a746-efcc7a674946logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Die beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der [[Aussagenlogik]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Flogseq____&quot;,272,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,239,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Hlogseq____&quot;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Hlogseq____&quot;,239,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-7807-4644-864a-8394e90a90b8logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n(p\\\\land q)\\\\land r logseq____&amp;\\\\equiv p\\\\land(q\\\\land r),\\\\quadlogseq____&amp;\\\\text{schreibe daher: }  p\\\\land q\\\\land r,\\\\quad \\\\land \\\\text{ assoziativ}\\\\\\\\\\n(p \\\\lor q) \\\\lor r logseq____&amp;\\\\equiv p \\\\lor (q\\\\lor r),\\\\quadlogseq____&amp;\\\\text{schreibe daher: } p\\\\lor q\\\\lor r,\\\\quad \\\\lor \\\\text{ assoziativ}\\\\\\\\\\np \\\\land q logseq____&amp;\\\\equiv q \\\\land p,\\\\quad \\\\land logseq____&amp;\\\\text{ kommutativ}\\\\\\\\\\np \\\\lor q logseq____&amp;\\\\equiv q \\\\lor p,\\\\quad \\\\lor logseq____&amp;\\\\text{ kommutativ}\\\\\\\\\\n\\\\neg(\\\\neg p) logseq____&amp;\\\\equiv p, \\\\quad \\\\neg logseq____&amp;\\\\text{ idenpotent}\\\\\\\\\\np\\\\land(q\\\\lor r)logseq____&amp;\\\\equiv (p\\\\land q)\\\\lor(p\\\\land r);\\\\notag\\\\\\\\\\np\\\\lor(q\\\\land r)logseq____&amp;\\\\equiv (p\\\\lor q)\\\\lor(p\\\\land r),\\\\quad logseq____&amp;\\\\land,\\\\lor\\\\text{ wechselseitig distributiv}\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&amp;\\\\equiv(\\\\neg p)\\\\lor(\\\\neg q);\\\\notag\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&amp;\\\\equiv(\\\\neg p)\\\\land (\\\\neg q), \\\\quad logseq____&amp;\\\\text{ (kleine) de Morgansche Regeln}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Flogseq____&quot;,246,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Vlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-7156-431e-af48-8039af796850logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Betrachte $\\logseq____&quot;xlogseq____&lt;y\\logseq____&quot;$ als AF über $\\\\Reals, 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$p(x)$ AF in der Variablen $x$ über $U$:logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Flogseq____&quot;,274,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-4c04-490a-bf96-aa1b5cdf7dc3logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Flogseq____&quot;,256,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Hlogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d8-e35c-42fd-a45f-ba71ae7e07bdlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\logseq____&quot;\\\\text{x ist prim}\\logseq____&quot; \\\\quad logseq____&amp; \\\\text{ist AF mit Variablen x über den  natürlichen Zahlen}\\\\\\\\\\n\\logseq____&quot;\\\\underbrace{x}_{x_1}logseq____&lt;\\\\underbrace{y}_{x_2}\\logseq____&quot;\\\\quad logseq____&amp;\\\\text{ist AF mit Variablen }x,y\\\\text{ über die reellen Zahlen } \\\\underbrace{\\\\Reals}_{U_1},\\\\underbrace{\\\\Reals}_{U_2}\\\\\\\\\\n\\logseq____&quot;\\\\text{x ist wahr}\\logseq____&quot;\\\\quadlogseq____&amp;\\\\text{ist AF mit Variablen x über dem Universum der Aussagen}\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^Flogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[274,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652fe1d9-1e4d-4898-a42d-cd381499e0c9logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[275,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche 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= Beweisende, auch [q.e.d.]([[Q.E.D.]]), [[w.z.b.w.]], QED, 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[[Regeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[277,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[277,logseq____&quot;^Flogseq____&quot;,251,536870923]],[logseq____&quot;^15logseq____&quot;,[277,logseq____&quot;^Xlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[277,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[277,logseq____&quot;^Ulogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[277,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[277,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[277,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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