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x=-\\\\frac{11}{12}\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Flogseq____&quot;,85,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Vlogseq____&quot;,85,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,30,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-528a-4760-8ed6-e9aea4a1a182logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\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;,[50,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Flogseq____&quot;,63,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Vlogseq____&quot;,87,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,38,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,44,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-f64e-4443-aa40-886451a3841elogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Satz von Vieta]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&amp;=0 logseq____&amp;logseq____&amp; \\\\text{habe }x_{1,2}\\\\text{ als Lösung}\\\\\\\\\\nx_1+x_2logseq____&amp;=-p logseq____&amp;logseq____&amp; x_1*x_2=q\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Flogseq____&quot;,92,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Vlogseq____&quot;,66,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Hlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-273c-4915-a163-4ef2c81e8c3blogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Logarithmen]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Flogseq____&quot;,60,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Vlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,31,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Potenzen]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Flogseq____&quot;,95,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Vlogseq____&quot;,95,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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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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logseq____&amp;x_1=3;logseq____&amp;x_2=-3\\\\\\\\\\n\\\\end{array}\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Flogseq____&quot;,51,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Vlogseq____&quot;,66,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-31f9-4fdf-85ed-a64a2cbdec09logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Wurzeln]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Flogseq____&quot;,52,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Vlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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a}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Flogseq____&quot;,68,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Vlogseq____&quot;,52,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,31,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-3ac0-41a5-b1c3-867d83fa50e9logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[59,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;,[59,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Flogseq____&quot;,57,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Vlogseq____&quot;,57,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-2ee1-40b3-9329-a04afa58422elogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[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;,65,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Vlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Hlogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-d8f9-4e7d-aeb8-1304bc38cac2logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[61,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;,[61,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Flogseq____&quot;,53,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Vlogseq____&quot;,53,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-4c39-408d-87ad-d1c2f223acf9logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____&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;,78,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Vlogseq____&quot;,78,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,32,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Hlogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-2ab9-4bdc-8655-1a42829a9b0clogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[63,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;,[63,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Flogseq____&quot;,87,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Vlogseq____&quot;,87,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,38,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,44,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-6f01-4eb7-ac78-61aca8b40ee6logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[64,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;,[64,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Flogseq____&quot;,59,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Vlogseq____&quot;,57,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-d094-4e0b-9fc5-66d6263372a3logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Links]]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;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Vlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,43,536870919]],[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;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^17logseq____&quot;,false,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-01f2-4216-bd6c-bf53a9ba1e56logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[pq-Formel]]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;,79,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Vlogseq____&quot;,88,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Hlogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-dc58-4679-906a-5bf6563f1a57logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{array}{c} (a+b)^0logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;1 \\\\\\\\\\n(a+b)^1logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;1 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^2logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 2 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^3logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;1 logseq____&amp;logseq____&amp; 3 logseq____&amp;logseq____&amp; 3 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^4logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 4 logseq____&amp;logseq____&amp; 6 logseq____&amp;logseq____&amp; 4 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^5logseq____&amp;logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 5 logseq____&amp;logseq____&amp; 10 logseq____&amp;logseq____&amp; 10 logseq____&amp;logseq____&amp; 5 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^6logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 6 logseq____&amp;logseq____&amp; 15 logseq____&amp;logseq____&amp; 20 logseq____&amp;logseq____&amp; 15 logseq____&amp;logseq____&amp; 6 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^7logseq____&amp;1 logseq____&amp;logseq____&amp; 7 logseq____&amp;logseq____&amp;21 logseq____&amp;logseq____&amp; 35 logseq____&amp;logseq____&amp; 35 logseq____&amp;logseq____&amp; \\\\cdots\\\\end{array}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;,90,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Vlogseq____&quot;,90,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-93bf-4397-a429-5dbb33f6ccfblogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[68,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;,[68,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Flogseq____&quot;,52,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Vlogseq____&quot;,52,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Ulogseq____&quot;,31,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-face-490b-9b31-b596cc1a6611logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Was ist Größer?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;,57,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Vlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-6a0d-4f0a-8924-5774a3a1dcbdlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Einsetzen, um zu überprüfen, ob man eine Fallunterscheidung brauchtlogseq____&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;,49,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Vlogseq____&quot;,85,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,30,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-51ed-4aba-bf4d-ec8f682ea359logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[71,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;,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Flogseq____&quot;,77,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Vlogseq____&quot;,77,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-be69-48a6-a346-eb4c98974de8logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[72,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 constraintlogseq____&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;,82,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Vlogseq____&quot;,82,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Hlogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-0e25-48bc-8fd8-1a096274dafdlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;https://www.wolframalpha.comlogseq____&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;,48,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Vlogseq____&quot;,48,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-5375-4156-a4b0-1a0c5f654960logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\n(a+b)^3(a^2+b^2)^3(a-b)^3logseq____&amp;=(a^2+b^2)^3\\\\left((a+b)(a-b)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=(a^2+b^2)^3(a^2-b^2)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=\\\\left((a^2+b^2)(a^2-b^2)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=(a^4-b^4)^3\\\\\\\\\\n\\\\frac{a-b}{(a+b)^{-1}}logseq____&amp;=(a-b)(a+b)\\\\notag\\\\\\\\\\nlogseq____&amp;=a^2-b^2\\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;,61,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Vlogseq____&quot;,53,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-2ec2-41bf-9d73-8bb34fddbdaelogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel}$\\n$\\\\text{Welche quadratische Gleichung hat die Lösung}$\\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;,[75,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Flogseq____&quot;,51,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Vlogseq____&quot;,51,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-42b1-464d-90c3-1145166a2aeelogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[76,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;,[76,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Flogseq____&quot;,55,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Vlogseq____&quot;,86,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-cc67-4afd-9dd5-7c734b136e75logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Trigonometrie]]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;,69,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Vlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Hlogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-2836-4b6a-8eb0-cb9c137827e9logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Binomialkoeffizient]]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;,89,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Vlogseq____&quot;,90,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,32,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Hlogseq____&quot;,32,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-e680-44cc-a148-9164287ba3b3logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nax^2+bx+clogseq____&amp;=0logseq____&amp;|:a\\\\quadlogseq____&amp;a\\\\ne0\\\\\\\\\\nx^2+\\\\frac ba x + \\\\frac ca logseq____&amp;= 0\\\\\\\\\\nplogseq____&amp;=\\\\frac ba,logseq____&amp;q = \\\\frac ca\\\\\\\\\\nx^2+px+qlogseq____&amp;=0\\n\\\\end{align}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;,88,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Vlogseq____&quot;,88,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-a15d-436b-ac17-83ea22cee611logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[80,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;,[80,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Flogseq____&quot;,71,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Vlogseq____&quot;,77,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-0123-4c31-bf36-ff191d30b558logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____&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;,89,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Vlogseq____&quot;,89,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Hlogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-40a4-4f66-b478-8a9063db9b2clogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Wurzeln]]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;,53,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Vlogseq____&quot;,95,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Hlogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774c-a7f2-4182-88d0-1bd27836a53flogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche }$[[Gleichungen]]$\\\\text{ sind richtig?}$\\n\\\\begin{align}\\ne^{x+y} logseq____&amp;= e^x + e^y logseq____&amp; ,f \\\\\\\\\\ne^{x+y} logseq____&amp;= e^x * x^y logseq____&amp; ,r \\\\\\\\\\ne^{x+y}logseq____&amp;=e^{xy} logseq____&amp; ,f\\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=x+y logseq____&amp; ,x+ylogseq____&gt;c 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logseq____&amp;\\\\text{ falls } y\\\\ge0\\\\\\\\\\n-y logseq____&amp;\\\\text{ falls } 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die \\logseq____&quot;[[Syntax]]\\logseq____&quot;, jetzt die [[Semantik]]. 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[[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Flogseq____&quot;,172,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Vlogseq____&quot;,172,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,164,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Hlogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Hlogseq____&quot;,164,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-04d5-425d-9e82-675d07089ed9logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Kontradiktion]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Flogseq____&quot;,188,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Vlogseq____&quot;,186,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Hlogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-4f48-4952-898e-7cfbfdaa47b0logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[175,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;,[175,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Flogseq____&quot;,191,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Vlogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-3677-4b62-af66-c63535f45d3elogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[176,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;,[176,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Flogseq____&quot;,186,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Vlogseq____&quot;,186,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Hlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-87dc-4f9a-b9ec-d83c1b2d60f0logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formeln $p,q$ [[logisch äquivalent]], wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Flogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Vlogseq____&quot;,186,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Hlogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Hlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Hlogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-c012-4d1d-8962-572e8562b79flogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 1. [[Aussagen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Flogseq____&quot;,192,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Vlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Hlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-f5d7-4ece-b1f9-ddc24b070a1dlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Flogseq____&quot;,169,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Vlogseq____&quot;,186,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,164,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Hlogseq____&quot;,164,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-2108-4516-bad2-098e98f67caalogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Weitere Beispiel}$\\n\\\\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;,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Flogseq____&quot;,183,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Vlogseq____&quot;,186,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-c26d-479a-bba2-4d26768d7b80logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\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;,[181,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Flogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Vlogseq____&quot;,186,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-4eab-432a-a22f-8c6640ef0811logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[182,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;,[182,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Flogseq____&quot;,185,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Vlogseq____&quot;,189,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,164,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Hlogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-d3f4-453c-b22e-0220e84959ealogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Flogseq____&quot;,177,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Vlogseq____&quot;,186,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Hlogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-3967-4279-9623-a09f6193be10logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Variable]], die den Wert $w$ oder $f$ annimmtlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Flogseq____&quot;,169,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Vlogseq____&quot;,169,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,151,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Hlogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-8292-4288-bb5b-eb42a41224cflogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Flogseq____&quot;,189,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Vlogseq____&quot;,189,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,161,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,164,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Hlogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Hlogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Hlogseq____&quot;,161,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Hlogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-137b-4521-8305-e30c75fc56adlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Verknüpfung von Aussagen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Flogseq____&quot;,175,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Vlogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Hlogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-0ffa-405a-90f0-5472bb3b456elogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $f$ istlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Flogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Vlogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-768d-4c8e-a443-bfa34746e05flogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Tantologie]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Flogseq____&quot;,189,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Vlogseq____&quot;,186,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Hlogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-fe92-40ac-bcb0-ef5fda99c6adlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Flogseq____&quot;,172,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Vlogseq____&quot;,186,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,164,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Hlogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Hlogseq____&quot;,164,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-0ab3-4d41-9f5e-27b23c4f22calogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Flogseq____&quot;,179,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Vlogseq____&quot;,179,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,163,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,164,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Hlogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Hlogseq____&quot;,163,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-7d79-4af9-8356-17525890da1blogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[191,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;,[191,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Flogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Vlogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Hlogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-25fc-419b-be8e-e32c43adabcclogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Büchertiplogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Flogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Vlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^17logseq____&quot;,false,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-0270-4f6a-8f72-344b9446b0f8logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $w$ istlogseq____&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;,188,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Xlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Vlogseq____&quot;,188,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6528774d-fe59-4189-a3ba-bf6625aabad4logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;C. Meinel, M. Mundhenk,  [[\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. Auflage 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[[Potenzen]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Flogseq____&quot;,60,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Vlogseq____&quot;,60,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Logarithmen]]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;,87,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Vlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,31,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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constraintlogseq____&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;,65,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Vlogseq____&quot;,65,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Hlogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-4ae8-4143-8840-36839d36e742logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;https://www.wolframalpha.comlogseq____&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;,49,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Vlogseq____&quot;,49,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-93aa-4cf3-82ff-e98d6460cd93logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;![draws/2023-10-08-21-23-31.excalidraw](../assets/excalidraw_svg/2023-10-08-21-23-31.svg)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;,72,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Vlogseq____&quot;,87,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-0d74-4484-84a7-99fc5186f2bflogseq____&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;,58,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Vlogseq____&quot;,60,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[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;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-0047-4c49-bd17-bd97c0cf5360logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\n(a+b)^3(a^2+b^2)^3(a-b)^3logseq____&amp;=(a^2+b^2)^3\\\\left((a+b)(a-b)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=(a^2+b^2)^3(a^2-b^2)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=\\\\left((a^2+b^2)(a^2-b^2)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=(a^4-b^4)^3\\\\\\\\\\n\\\\frac{a-b}{(a+b)^{-1}}logseq____&amp;=(a-b)(a+b)\\\\notag\\\\\\\\\\nlogseq____&amp;=a^2-b^2\\n\\\\end{align}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;,98,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Vlogseq____&quot;,58,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-6d01-4207-af7a-c1961e372b50logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[67,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;,[67,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Flogseq____&quot;,61,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Vlogseq____&quot;,61,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Ulogseq____&quot;,31,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-f2c5-4ee6-a81d-74dbf0393bb8logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[68,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;,[68,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Flogseq____&quot;,96,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Vlogseq____&quot;,65,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-d51f-4a7f-96d5-74cf5614b79blogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Quadratische Gleichungen]]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;,65,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Vlogseq____&quot;,60,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Hlogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-02f4-4167-9abc-2ed780b13d3dlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\sqrt[n]{a^n}logseq____&amp;=1^\\\\frac nn=a^1=a\\\\\\\\\\n\\\\sqrt[n]{\\\\frac ab} logseq____&amp;= \\\\frac{\\\\sqrt[n]a}{\\\\sqrt[n]b}\\\\\\\\\\n\\\\left(\\\\sqrt[n]a\\\\right)^mlogseq____&amp;=a^\\\\frac mn\\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;,62,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[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;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-1238-4ddf-b890-0145cfabc803logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____&gt;0$ welche keinen Sinn ergibtlogseq____&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;,96,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Vlogseq____&quot;,96,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Hlogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-072c-4196-b569-6b4f661e05adlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche }$[[Gleichungen]]$\\\\text{ sind richtig?}$\\n\\\\begin{align}\\ne^{x+y} logseq____&amp;= e^x + e^y logseq____&amp; ,f \\\\\\\\\\ne^{x+y} logseq____&amp;= e^x * x^y logseq____&amp; ,r \\\\\\\\\\ne^{x+y}logseq____&amp;=e^{xy} logseq____&amp; ,f\\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=x+y logseq____&amp; ,x+ylogseq____&gt;c \\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=e^x*e^ylogseq____&amp;,f\\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=ln(e^x+y)logseq____&amp;,x+ylogseq____&gt;0\\n\\\\end{align}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;,87,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Vlogseq____&quot;,87,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,33,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Hlogseq____&quot;,33,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-7aa3-4c51-a0ad-bcbf3c6e66e1logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Wurzeln]]logseq____&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;,61,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Vlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Hlogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-8427-415f-b6dd-42d05b5cce5blogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel}$\\n$\\\\text{Welche quadratische Gleichung hat die Lösung}$\\n$x_1=3\\\\quad x_2=4$\\n\\\\begin{align}\\nx_1+x_2 = 7 logseq____&amp;= p logseq____&amp;, 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[[Pascalsches Dreieck]]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;,90,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Vlogseq____&quot;,54,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Nenner]]slogseq____&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;,68,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Vlogseq____&quot;,65,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,38,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,44,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Hlogseq____&quot;,38,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Hlogseq____&quot;,44,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-cec2-4b89-ba17-be9654fa309clogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____&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;,85,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Vlogseq____&quot;,85,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Hlogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-f7d9-4cd7-9af3-2ee53301c3d6logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\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 x)^5logseq____&amp;=2+20x+40x^2\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Flogseq____&quot;,81,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Vlogseq____&quot;,82,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-5b23-4a27-b3de-fc56f94ef369logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nax^2+bx+clogseq____&amp;=0logseq____&amp;|:a\\\\quadlogseq____&amp;a\\\\ne0\\\\\\\\\\nx^2+\\\\frac ba x + \\\\frac ca logseq____&amp;= 0\\\\\\\\\\nplogseq____&amp;=\\\\frac ba,logseq____&amp;q = \\\\frac ca\\\\\\\\\\nx^2+px+qlogseq____&amp;=0\\n\\\\end{align}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;,69,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Vlogseq____&quot;,69,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-3576-4068-9886-094277a36cd0logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Potenzen]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Flogseq____&quot;,52,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Vlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Hlogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-e35d-4c35-9248-d407d61e87adlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[88,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;,[88,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Flogseq____&quot;,89,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Vlogseq____&quot;,93,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-f022-4b81-8a1c-caa92139a47clogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[89,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;,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Flogseq____&quot;,93,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Vlogseq____&quot;,93,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-6539-41d4-8d37-f1f3edc2ba58logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[90,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;,[90,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Flogseq____&quot;,75,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Vlogseq____&quot;,54,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-dd36-4857-9eef-73941fb86d12logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[91,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;,[91,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Flogseq____&quot;,47,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Vlogseq____&quot;,73,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-0895-432d-bf95-d1ce9947ec48logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[pq-Formel]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Flogseq____&quot;,86,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Vlogseq____&quot;,69,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Hlogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-74df-40ea-836f-4a1463ec3c71logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Trigonometrie]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Flogseq____&quot;,78,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Vlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Hlogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-a895-4d40-9039-f16526202efalogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[94,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;,[94,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Flogseq____&quot;,83,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Vlogseq____&quot;,83,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,38,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,44,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-27dc-4014-a119-560a08ac30f5logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Flogseq____&quot;,48,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Vlogseq____&quot;,48,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,32,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Hlogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a36-c3fd-452e-971d-88b49705867elogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\n\\\\sqrt{x^4+6x^2y+9y^2}logseq____&amp;=\\\\sqrt{(x^2+3y)^2}=x^2+3y\\\\\\\\\\n\\\\sqrt {x + \\\\sqrt{x^2-y^2}}\\\\sqrt{x-\\\\sqrt{x^2-y^2}}logseq____&amp;=\\\\sqrt{\\\\left(x + 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$\\\\sin^{-2}x+cos^2y=1,r$ ist 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^15logseq____&quot;,[105,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;auffrischung 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Lösung mit 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logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870920]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Jlogseq____&quot;,[],536870920]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Hlogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^17logseq____&quot;,false,536870920]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-dd8d-4ee4-9640-6e7f47660a25logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[110,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;,[110,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Flogseq____&quot;,129,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Xlogseq____&quot;,105,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Vlogseq____&quot;,108,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ulogseq____&quot;,100,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ulogseq____&quot;,101,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ulogseq____&quot;,104,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ulogseq____&quot;,105,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ulogseq____&quot;,106,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-89d1-4885-9f92-75447d2de19alogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Der [[Betrag]] ist der [[Abstand]] zu 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Fall}\\\\quad 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[[Kontradiktion]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Flogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Vlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Ulogseq____&quot;,143,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Hlogseq____&quot;,143,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-4082-4a3e-9f7b-fbeb0e6efbf6logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $f$ istlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Flogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Vlogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Ulogseq____&quot;,143,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-20f9-4bca-a5cd-b8581e0a471blogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[160,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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$p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Flogseq____&quot;,175,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Vlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Hlogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-8cd6-451f-930e-6a23252270e3logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Verknüpfung von Aussagen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Flogseq____&quot;,164,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Vlogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Hlogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-7d39-4c2f-a273-bb6da930a38blogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;C. Meinel, M. Mundhenk,  [[\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. Auflage 2011]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Flogseq____&quot;,169,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Vlogseq____&quot;,169,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Hlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-499e-49a1-9c0e-4cb3fbad5b14logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[164,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;,[164,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Flogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Vlogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-e9c5-4b94-963a-7d974d2d9b40logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wikipedia]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Flogseq____&quot;,163,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Vlogseq____&quot;,169,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Hlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-46e0-4d12-a18c-1eb4b6e1cc40logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Flogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Vlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Hlogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-54e2-46d8-9eec-4f10f139a6ddlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 1. [[Aussagen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Flogseq____&quot;,169,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Vlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^17logseq____&quot;,false,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-4dab-41c3-8e67-66480d772811logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Tantologie]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Flogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Vlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Hlogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-3673-401b-b805-92751e7df1eblogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Flogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Vlogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,149,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Hlogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Hlogseq____&quot;,149,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-6cbc-4745-b3dd-8acb1fa2a6bdlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\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;,[172,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Flogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Vlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-e4fb-4b08-8148-2e45fd7cf997logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $w$ istlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Flogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Vlogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-0565-42b3-9c11-6e8ff2d6f431logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Belegung]] (der [[Variablen]])logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Flogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Vlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,144,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Hlogseq____&quot;,144,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Hlogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-866e-47f7-b139-36e6710f6ef1logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formeln $p,q$ [[logisch äquivalent]], wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Flogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Vlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,136,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,146,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Hlogseq____&quot;,136,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Hlogseq____&quot;,146,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Hlogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-2e72-4ac7-9ab3-cd4d0c87cdf0logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Zuordnung von $w/f$ an jede [Variable](Variablen) einer [[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Flogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Vlogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,144,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Hlogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-b719-4ea4-99e7-71c4d27e7830logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[177,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;,[177,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Flogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Vlogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,136,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Hlogseq____&quot;,136,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-8bbb-46b8-b8bf-c185cd634152logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[178,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;,[178,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Flogseq____&quot;,172,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Vlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,145,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,151,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Hlogseq____&quot;,145,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Hlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Hlogseq____&quot;,151,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-aace-499b-bfdc-6e700e3257aflogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Weitere Beispiel}$\\n\\\\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;,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Flogseq____&quot;,161,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Vlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-0531-43b6-9b90-657c352c5a3alogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Flogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Vlogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,136,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,139,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,140,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Hlogseq____&quot;,139,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Hlogseq____&quot;,140,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Hlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Hlogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-f324-49e4-9606-7301eb7dc8a6logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Klogseq____&quot;,1697188407493,536870923]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;regelnlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^11logseq____&quot;,logseq____&quot;Regelnlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Blogseq____&quot;,1697188407493,536870923]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-8af2-40eb-b670-de3a601c19c5logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Klogseq____&quot;,1697188407486,536870923]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;de 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[[Allquantor]] 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beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache](Sprachen) der [[Aussagenlogik]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Flogseq____&quot;,215,536870923]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Xlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,185,536870923]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Hlogseq____&quot;,185,536870923]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-fa49-49a8-bbfa-3cdf0ac33f9blogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Regeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Flogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Xlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Vlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,182,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Hlogseq____&quot;,182,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^17logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-bf8d-4990-8385-f42c36d8454flogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[203,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;,[203,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Flogseq____&quot;,205,536870923]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Xlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-e6e1-4837-9285-ea9b357c1593logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[204,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;,[204,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Flogseq____&quot;,201,536870923]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Xlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-ae16-41a4-8348-1b7a11752444logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Flogseq____&quot;,212,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Xlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,100,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Hlogseq____&quot;,100,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-bcfb-467e-a3a4-9eb79c76e36flogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Endliches Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Flogseq____&quot;,204,536870923]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Xlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-d15b-4ef8-b3f7-f28b06e02044logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[207,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;,[207,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Flogseq____&quot;,203,536870923]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Xlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Vlogseq____&quot;,203,536870923]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ulogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-7c88-4368-bc91-10a37bb720f8logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[208,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;,[208,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Flogseq____&quot;,206,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Xlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-5b99-4bef-9ad5-b0d0487aeb60logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Aussageform]] (AF) über [Universen](Universen (Logik)) $U_1,\\\\cdots,U_n$:logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Flogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Xlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ulogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Hlogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-b0fa-4ae1-99e2-83e4b6bc50e3logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Schachtelung von quantoren ([Beispiel](Beispiele)):logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Flogseq____&quot;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Xlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Vlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,182,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-e5b0-425c-a9ca-4be578d5257dlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[211,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;,[211,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Flogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Xlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Vlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,182,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-d966-4cf8-88ff-1271b7e114aclogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[212,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;,[212,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Flogseq____&quot;,209,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Xlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,144,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,198,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Hlogseq____&quot;,144,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Hlogseq____&quot;,198,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-c8d8-4ba2-af18-76bbe1285f94logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[213,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;,[213,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Flogseq____&quot;,202,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Xlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Vlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-f0be-43f8-af47-72e17c2bf159logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche Regeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Flogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Xlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Vlogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,183,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,186,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,189,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,193,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,194,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Hlogseq____&quot;,183,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Hlogseq____&quot;,186,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Hlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Hlogseq____&quot;,189,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Hlogseq____&quot;,193,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Hlogseq____&quot;,194,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-79a6-4370-8ec7-e6fe0bb51ee7logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x)$ AF in der Variablen $x$ über $U$:logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Flogseq____&quot;,203,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Xlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ulogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-d545-44bd-8c78-124a1b9a85f9logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativschreibweisen:\\n$\\\\forall x: p(x)$ auch $\\\\bigger\\\\land x:p(x)$\\n$\\\\exists x:p(x)$ auch $\\\\bigger\\\\lor x:p(x)$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Flogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Xlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ulogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-63c4-4505-b499-5f1755503a38logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\exists x:p(x)$ ist 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[[Aussageform]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Flogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Xlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Vlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Ulogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Hlogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-e4a4-4424-abaa-e65d8c40cccflogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[219,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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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 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[[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Flogseq____&quot;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Xlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Vlogseq____&quot;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Ulogseq____&quot;,182,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Ulogseq____&quot;,184,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Ulogseq____&quot;,192,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Ulogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Hlogseq____&quot;,184,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Hlogseq____&quot;,192,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Hlogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65290a37-f9de-4c04-866f-462c19b132a2logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Gleichartige](Gleichartig) [[Quantoren]] dürfen [vertieft](vertiefen) 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[[Regeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^Flogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^Xlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^Ulogseq____&quot;,182,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^Ulogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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