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x_1*x_2=q\\\\\\\\\\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;,75,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Vlogseq____&quot;,73,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Hlogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-9b06-4d31-9751-e1d06d3c1194logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Pascalsches Dreieck]]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;,55,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Vlogseq____&quot;,93,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Hlogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-fa9f-4813-bad1-854aeabea4dclogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche quadratische Gleichung hat die Lösung}$\\n$x_1=3\\\\quad x_2=4$\\n\\\\begin{align}\\nx_1+x_2 = 7 logseq____&amp;= p logseq____&amp;, x_1x_2=12=q\\\\\\\\\\nx^2+px+qlogseq____&amp;=0\\\\\\\\\\nx^2-7x+12logseq____&amp;=0\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Flogseq____&quot;,99,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Vlogseq____&quot;,99,536870919]],[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;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-d3b8-4afd-8aa2-3410c33eb3cclogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[52,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;,[52,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Flogseq____&quot;,54,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Vlogseq____&quot;,54,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,33,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Hlogseq____&quot;,33,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-531a-42a1-b0e1-44d0c2f0d477logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;https://www.wolframalpha.comlogseq____&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;,76,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Vlogseq____&quot;,76,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,44,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,46,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-443c-4725-aed5-952633fa3e9clogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Potenzen]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Flogseq____&quot;,47,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Hlogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-56a5-427a-9fbc-5146de78354clogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[55,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;,[55,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Flogseq____&quot;,68,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Vlogseq____&quot;,93,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-39c6-46e7-b41d-c00f228155c9logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____&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;,92,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Vlogseq____&quot;,92,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,32,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,38,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Hlogseq____&quot;,38,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-3544-4149-a362-2c53d7073fc1logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[57,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;,[57,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Flogseq____&quot;,65,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Vlogseq____&quot;,90,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-238a-46d9-add3-4e585f263030logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;cosa -logseq____&gt; beliebige Variable\\ncubus -logseq____&gt; hoch 3logseq____&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;,86,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Vlogseq____&quot;,86,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-473a-47f4-9953-abbb3f7a12eelogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\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;,[59,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Flogseq____&quot;,63,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Vlogseq____&quot;,63,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-d5fd-4e5b-afdd-2389d11246bclogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[60,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;,[60,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Flogseq____&quot;,69,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Vlogseq____&quot;,95,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-b38a-4ac1-b23d-f7b15c712725logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]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;,64,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Vlogseq____&quot;,50,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Hlogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-12cf-41b6-ab33-df2f9df7871dlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[62,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;,[62,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Flogseq____&quot;,100,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Vlogseq____&quot;,100,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-7eaa-4be4-b262-b2bf08e1b435logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]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;,72,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Vlogseq____&quot;,66,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Hlogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-ad68-4513-8aea-70407ef75d71logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{array}{c} 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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;,[64,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Flogseq____&quot;,50,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Vlogseq____&quot;,50,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-f80d-4a86-95e2-9731ef7bd6ddlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[65,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;,[65,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Flogseq____&quot;,90,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Vlogseq____&quot;,90,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Hlogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-4a30-4622-942a-8de45fd75e61logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Potenzen]]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;,70,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Vlogseq____&quot;,70,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Hlogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-1c99-4d8e-ac00-6a3fda0791d1logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Logarithmen]]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;,54,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Ulogseq____&quot;,31,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Hlogseq____&quot;,31,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-efda-433a-a314-fbea7ade8ad7logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Allgemein}$\\n\\\\begin{align}\\n(a+b)^2logseq____&amp;=a^2+2ab+b^2logseq____&amp;,\\\\text{ 1. Binomische Formel}\\\\\\\\\\n(a-b)^2logseq____&amp;=a^2-2ab+b^2logseq____&amp;,\\\\text{ 2. Binomische Formel}\\\\\\\\\\n(a+b)(a-b)logseq____&amp;=a^2-b^2logseq____&amp;,\\\\text{ 3. Binomische Formel}\\\\\\\\\\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;,93,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Vlogseq____&quot;,93,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-82c3-4848-9194-55e314a9b102logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[69,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;,[69,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Flogseq____&quot;,95,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Vlogseq____&quot;,95,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-7ed5-4367-9fff-3e7f189f7615logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Potenzen]] und [[Wurzeln]]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;,93,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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\\\\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;,[82,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Flogseq____&quot;,81,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Vlogseq____&quot;,81,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-e145-4673-9b6d-236b26670585logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[83,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;,[83,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Flogseq____&quot;,52,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Vlogseq____&quot;,54,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-1552-42a7-aba4-d512365902bclogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Rationalmachen]] des [[Nenner]]slogseq____&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;,48,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Vlogseq____&quot;,90,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Hlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Hlogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-161d-429a-a0fb-f941bac3964elogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[85,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;,[85,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Flogseq____&quot;,67,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Vlogseq____&quot;,67,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,31,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-b6b4-4be7-8f99-5c8897bfae46logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Alte Schreibweise}$\\n\\\\begin{align}\\n\\\\text{cosa }logseq____&amp;\\\\text{plus }logseq____&amp;\\\\text{cubus }logseq____&amp;\\\\text{acq }logseq____&amp;6\\\\\\\\\\nxlogseq____&amp;+logseq____&amp;x^3logseq____&amp;=logseq____&amp;6\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Flogseq____&quot;,63,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Vlogseq____&quot;,66,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-af1d-4c13-87e1-e9027bb14a4flogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Quadratische Gleichungen]]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;,90,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Vlogseq____&quot;,70,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[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;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-2d24-46bf-b137-06e2ca87ad49logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[88,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;,[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;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Vlogseq____&quot;,80,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Hlogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-e8ec-40e5-a898-5721570e5d9dlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\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 + \\\\sqrt{x^2-y^2}\\\\right)\\\\left(x-\\\\sqrt{x^2-y^2}\\\\right)}\\\\notag\\\\\\\\\\nlogseq____&amp;=\\\\sqrt{x^2-(x^2-y^2)}\\\\notag\\\\\\\\\\nlogseq____&amp;=\\\\sqrt{y^2}=\\\\left|y\\\\right|\\\\\\\\\\n\\\\sqrt[5]{a\\\\sqrt[3]a}=\\\\sqrt[5]{\\\\sqrt[3]{a^3}\\\\sqrt[3]a}\\nlogseq____&amp;=\\\\sqrt[5]{\\\\sqrt[3]{a^4}}\\n=\\\\sqrt[5]{a^\\\\frac43}\\n=a^{\\\\frac43\\\\frac15}=a^\\\\frac4{15}\\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;,80,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Vlogseq____&quot;,80,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-0f83-4a7f-8084-9d0f75a6d566logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Wurzeln]]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;,66,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Vlogseq____&quot;,70,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Hlogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-fef8-4bdd-8203-f674bda2d3a8logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[91,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;,[91,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Flogseq____&quot;,102,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Vlogseq____&quot;,61,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Hlogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-45b5-46a5-b8d7-179320ca7102logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Binomialkoeffizient]]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;,61,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Vlogseq____&quot;,50,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,32,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[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;,32,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-c6a4-46a2-ab07-b5b37bbb1334logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Binomische Formeln]]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;,95,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[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;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-1797-4fb6-aed2-e4e8301af79flogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Wurzelgleichung]]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;,87,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Vlogseq____&quot;,70,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,30,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Hlogseq____&quot;,30,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-012e-438d-941f-33508d24ee00logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Trigonometrie]]logseq____&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;,71,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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a + \\\\ln b logseq____&amp;= \\\\ln(a*b) \\\\\\\\\\n\\\\ln(-a) logseq____&amp;= \\\\frac1{\\\\ln 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Wissensabgleich [[Wurzeln]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Flogseq____&quot;,67,536870919]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Flogseq____&quot;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Vlogseq____&quot;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Jlogseq____&quot;,[],536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Hlogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-f372-429e-92e2-3dde5ec084bdlogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Flogseq____&quot;,156,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Vlogseq____&quot;,116,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Hlogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-a244-4e3d-a3a6-410e2d8368d4logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 1a}\\\\quad x\\\\ge -2$\\n\\\\begin{align}\\n|x+2|logseq____&amp;=x+2\\\\\\\\\\nx-3logseq____&amp;\\\\le x+2 logseq____&amp;|logseq____&amp;+3-x\\\\\\\\\\n0logseq____&amp;\\\\le5\\\\\\\\\\n\\\\end{align}\\n\\\\begin{align}\\nL_1=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|x\\\\ge3,x\\\\ge-2,0\\\\le5\\\\right\\\\}=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|x\\\\ge3\\\\right\\\\}=[3,\\\\infty)\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Flogseq____&quot;,134,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Vlogseq____&quot;,125,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-4399-4f98-a7b5-b402ed87d4b0logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]\\n\\\\begin{align}\\n|5|=logseq____&amp;5\\\\\\\\\\n|-3,3|logseq____&amp;=3,3\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Flogseq____&quot;,151,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Vlogseq____&quot;,145,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Hlogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-ce66-45d1-86a1-436142010558logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Flogseq____&quot;,143,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Vlogseq____&quot;,143,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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aller rellen Zahlen zwischen 4 und $\\\\infty$ ohne 4 und 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logseq____&amp;|logseq____&amp; *(-1)\\\\\\\\\\nxlogseq____&amp;logseq____&gt;11\\n\\\\end{align}\\n\\\\begin{align}\\nL_3=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|xlogseq____&gt;3,xlogseq____&gt;11\\\\right\\\\}=(11,\\\\infty)\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^Flogseq____&quot;,117,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^Vlogseq____&quot;,138,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-4adb-4885-b380-a6a7879e9badlogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Kombinieren:\\n\\\\begin{align}\\nLlogseq____&amp;=L_1\\\\cup L_2\\\\cup L_3=\\\\left(-\\\\infty,\\\\frac13\\\\right)\\\\cup\\\\left(11,\\\\infty\\\\right)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Flogseq____&quot;,146,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Vlogseq____&quot;,138,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[147,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-266a-4824-8fe5-6c7217160da5logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[148,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 2b}\\\\quad xlogseq____&lt;-2$\\n\\\\begin{align}\\n|\\\\underbrace{x+2}_{logseq____&lt;0}logseq____&amp;=-(x+2)=-x-2\\\\\\\\\\n-x+3logseq____&amp;\\\\le -x-2 logseq____&amp;|logseq____&amp;+x\\\\\\\\\\n3logseq____&amp;\\\\le-2logseq____&amp;logseq____&amp;\\\\underset{falsche 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2a}\\\\quad x\\\\ge-2$\\n\\\\begin{align}\\n|\\\\underbrace{x+2}_{\\\\ge0}logseq____&amp;=x+2\\\\\\\\\\n-x+3logseq____&amp;\\\\le x+2 logseq____&amp;|logseq____&amp; -2\\\\\\\\\\n-x+1logseq____&amp;\\\\le x logseq____&amp;|logseq____&amp; +x\\\\\\\\\\n\\\\frac12logseq____&amp;\\\\le x logseq____&amp;|logseq____&amp; :2\\\\\\\\\\n\\\\end{align}\\n\\\\begin{align}\\nL_2=\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|xlogseq____&lt;3,x\\\\ge-2,x\\\\ge\\\\frac12\\\\right\\\\}=\\\\left[\\\\frac12,3\\\\right)\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Flogseq____&quot;,140,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Vlogseq____&quot;,125,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-28a6-49f9-8a68-98223b615cfclogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Menge aller reellen Zahlen zwischen 1 und 4 ohne 1 und 4\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-1logseq____&lt;xlogseq____&lt;4\\\\right\\\\}=:\\\\underbrace{(-1,4)}_\\\\text{Offenes 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[[Betrag]] ist der [[Abstand]] zu 0\\n\\\\begin{align}\\nf(x)=logseq____&amp;|x|:=logseq____&amp;\\\\begin{cases}\\nxlogseq____&amp;x\\\\ge0\\\\\\\\\\n-xlogseq____&amp;xlogseq____&lt;0\\n\\\\end{cases}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Flogseq____&quot;,145,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Vlogseq____&quot;,145,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Ulogseq____&quot;,110,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Hlogseq____&quot;,110,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Hlogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-462d-4e22-bdce-fe3edbdab8d4logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Flogseq____&quot;,133,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Vlogseq____&quot;,142,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-a0c5-4371-8139-e57058c3f496logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;**oder** $\\\\rightarrow$ 5 ist abstand von x zu -3logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Flogseq____&quot;,121,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Vlogseq____&quot;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-0494-421d-96d1-862e26dcd271logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[154,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 1}\\\\quad xlogseq____&lt;3$\\n\\\\begin{align}\\n|x-3|logseq____&amp;=-x+3\\\\\\\\\\n-x+3logseq____&amp;logseq____&lt;5 logseq____&amp;|logseq____&amp;-3\\\\\\\\\\n-xlogseq____&amp;logseq____&lt;2 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der Gleichung }x^2+\\\\underbrace{4}_p 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von $w/f$ an jede [Variable]([[Variablen]]) einer [[Aussageformel]]logseq____&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;,191,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Vlogseq____&quot;,191,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Hlogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Hlogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-2bd4-4be1-9afd-5a49eb8ab1c4logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussageformel]]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;,200,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Vlogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[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;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-6079-4cdd-b774-1bce4b044c79logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $w$ istlogseq____&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;,192,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Vlogseq____&quot;,192,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-ec60-4dbc-b054-c11c91495cddlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Weitere [[Beispiele]]logseq____&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;,199,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Vlogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Hlogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-0559-47f2-bc76-f7bd97a6644flogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Belegung]] (der [[Variablen]])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;,188,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Vlogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Hlogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Hlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-d4bb-4742-9eda-40367c9a6af8logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Tantologie]]logseq____&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;,202,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Vlogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Hlogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-8ec6-4557-8624-f70f2ffe53c7logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[193,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;,[193,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Flogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Vlogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Hlogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-f2fa-41f7-a1f2-c7ee1a88cd40logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $f$ istlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Flogseq____&quot;,196,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Vlogseq____&quot;,196,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,169,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-2bdb-476d-8dd9-8dc5ca1a3953logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 1. [[Aussagen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Flogseq____&quot;,181,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Vlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Hlogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-829a-47cc-9dee-322478f458e0logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Kontradiktion]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Flogseq____&quot;,192,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Vlogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,169,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Hlogseq____&quot;,169,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-7dab-428c-b2aa-fa6da21f6e6clogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Flogseq____&quot;,202,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Vlogseq____&quot;,202,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Hlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Hlogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Hlogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Hlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-76f2-4e35-a678-d881faa1bfd3logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[198,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;,[198,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Flogseq____&quot;,205,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Vlogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,171,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,177,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Hlogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Hlogseq____&quot;,171,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Hlogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Hlogseq____&quot;,177,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-1a22-4c9b-bb0c-d124c5f8b092logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Flogseq____&quot;,203,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Vlogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Hlogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-71fc-4764-84ae-d2a6abc5fd2dlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussagenlogische Variable]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Flogseq____&quot;,198,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Vlogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,163,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Flogseq____&quot;,191,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Vlogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Hlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Hlogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-ebf0-47b4-a29f-ac9fb3e44fe6logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formeln $p,q$ [[logisch äquivalent]], wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv 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die den Wert $w$ oder $f$ annimmtlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Flogseq____&quot;,200,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Vlogseq____&quot;,200,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,163,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Hlogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f13-7024-48e6-8f33-a0dfc918c984logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;C. Meinel, M. Mundhenk, [[\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. Auflage 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durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt 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morgansche regelnlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^11logseq____&quot;,logseq____&quot;de Morgansche 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[[Existenzquantor]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Flogseq____&quot;,254,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Vlogseq____&quot;,254,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Hlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Hlogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-3389-482d-b779-58a774e9d48clogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Verschiedene [[Quantoren]] dürfen **nicht** vertauscht werdenlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Flogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Vlogseq____&quot;,269,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Hlogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-5ab0-43d2-8ac3-32197af008f7logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[238,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;,[238,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Flogseq____&quot;,258,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Vlogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-7326-4e4b-b315-df4cd09edc63logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[239,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;,[239,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Flogseq____&quot;,273,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Vlogseq____&quot;,273,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-f583-4bd9-834a-315abadd9670logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $x$ aus $\\\\Reals$ beliebig. Setze $y:=x+1$ (ist aus $\\\\Reals$). Dann ist $xlogseq____&lt;x+1=y$ also $xlogseq____&lt;y$. $\\\\blacksquare$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Flogseq____&quot;,252,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Vlogseq____&quot;,252,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-5e58-4b5e-91c6-8bc707ea0a0alogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativschreibweisen:\\n$\\\\forall x: p(x)$ auch $\\\\bigwedge x:p(x)$\\n$\\\\exists x:p(x)$ auch $\\\\bigvee x:p(x)$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Flogseq____&quot;,272,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Vlogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-daf8-4d48-8c7c-e5d02c0592d8logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\forall x:p(x)$ ist die [Aussage]([[[]Aussagen]]): $\\logseq____&quot;\\\\text{Für alle x aus U ist p(x) wahr}\\logseq____&quot;\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w\\\\quadlogseq____&amp;\\\\text{fallls p(x) w für alle x aus U}\\\\\\\\f\\\\quadlogseq____&amp;\\\\text{falls p(x) f für (wenigstens) ein x aus U}\\\\end{cases}$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Flogseq____&quot;,268,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Vlogseq____&quot;,268,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,166,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Hlogseq____&quot;,166,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Hlogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-f457-4b60-8b84-3925cf8c708alogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Flogseq____&quot;,266,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Vlogseq____&quot;,266,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,230,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Hlogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Hlogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Hlogseq____&quot;,230,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-4ef2-4ee8-926a-81b6ee2a0428logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Regeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Flogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Vlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Hlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^17logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-4231-421c-b66f-ded17870b441logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Aussageform]] (AF) über [Universen]([[Universen (Logik)]]) $U_1,\\\\cdots,U_n$:logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Flogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Vlogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Hlogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Hlogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-a779-4c0d-810a-d48321050ba3logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Flogseq____&quot;,251,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Vlogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Hlogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-7f52-499d-ba10-18b0c65450a4logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,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;,[247,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Flogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Vlogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-595d-4e88-87a4-436e1801243flogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[248,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;,[248,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Flogseq____&quot;,244,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Vlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-2426-4cd7-b351-0432485e18a1logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[249,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 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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;,[251,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Flogseq____&quot;,245,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Vlogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,170,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,174,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,231,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Hlogseq____&quot;,170,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Hlogseq____&quot;,174,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Hlogseq____&quot;,231,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Hlogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-6c50-4181-8137-1391d3d88b5elogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist 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[[Regeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Flogseq____&quot;,241,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Vlogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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p(0_m)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Flogseq____&quot;,260,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Vlogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-c439-439b-bf1c-3488a23676a4logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Betrachte 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$\\\\pi$ eine \\logseq____&quot;[[Permutation]]\\logseq____&quot; der Zahl $(1,2,\\\\cdots,n)$ 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beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der 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[[Quantoren]] dürfen vertauscht werdenlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Flogseq____&quot;,253,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Vlogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Hlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Hlogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-bd10-4bb9-9ee6-25eeab0ddccflogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Endliches Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Flogseq____&quot;,238,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Vlogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-06fc-4fe2-9e3a-77b77e67a0e4logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\blacksquare$ = Beweisende, auch [q.e.d.]([[Q.E.D.]]), [[w.z.b.w.]], QED, ![image.png](../assets/image_1697192491775_0.png)logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Flogseq____&quot;,240,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Vlogseq____&quot;,240,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,212,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,215,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Hlogseq____&quot;,212,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Hlogseq____&quot;,215,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-54ae-49b7-a2d8-d8469f3bc423logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Flogseq____&quot;,259,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Vlogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Hlogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-0622-4de8-8ed1-2de12b8d9e71logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Aussageform]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Flogseq____&quot;,248,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Vlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Hlogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-d411-4899-9506-082042c762d3logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist falsch}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Flogseq____&quot;,252,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Vlogseq____&quot;,255,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Hlogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-d213-4e33-a599-c18390cacb68logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche Regeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Flogseq____&quot;,248,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Vlogseq____&quot;,248,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,211,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,219,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,226,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Hlogseq____&quot;,211,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Hlogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Hlogseq____&quot;,219,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Hlogseq____&quot;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Hlogseq____&quot;,226,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Hlogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-c544-46eb-bc0c-a91e4a8acce0logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:(p(x)\\\\land q(x)) logseq____&amp;\\\\equiv (\\\\forall x: p(x)) \\\\land (\\\\forall x:q(x));\\\\notag\\\\\\\\\\n\\\\exists x: (p(x) \\\\lor q(x)) logseq____&amp;\\\\equiv (\\\\exists x: p(x))\\\\lor(\\\\exists x: q(x)),\\\\quadlogseq____&amp;\\\\text{Große Assoziativgesetze}\\\\\\\\\\n\\\\neg(\\\\forall x:p(x))logseq____&amp;\\\\equiv \\\\exists x: (\\\\neg p(x));\\\\quadlogseq____&amp;\\\\text{Große de Morgansche Regeln;}\\\\notag\\\\\\\\\\n\\\\neg(\\\\exists x: p(x)) logseq____&amp;\\\\equiv \\\\forall x: (\\\\neg p(x)),\\\\quadlogseq____&amp;\\\\text{Negationsregeln.}\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Flogseq____&quot;,253,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Vlogseq____&quot;,253,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-7728-468e-8db6-fb60a783f139logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nlogseq____&amp;\\\\neg\\\\left(\\\\forall x :\\\\exists y :\\\\forall w :\\\\forall u :\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)\\\\right)\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x:(\\\\neg(\\\\exists y: \\\\forall w: \\\\forall u: \\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x:\\\\forall y:(\\\\neg(\\\\forall w: \\\\forall u:\\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x:\\\\forall y:\\\\exists w:(\\\\neg(\\\\forall u:\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x: \\\\forall y: \\\\exists w: \\\\exists u : \\\\forall z:\\\\neg(p(x,y,z)\\\\rightarrow q(u,w))\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Flogseq____&quot;,262,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Vlogseq____&quot;,262,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-e491-45bf-8b75-574a33440d1elogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x)$ AF in der Variablen $x$ über $U$:logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Flogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Vlogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-b5ce-4051-a2f4-431506f9ba7clogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nlogseq____&amp;\\\\forall x: \\\\forall y: p(x, y) \\\\equiv \\\\forall y: \\\\forall x: p(x,y)\\\\\\\\\\nlogseq____&amp;\\\\exists x:\\\\exists y:p(x,y)\\\\equiv\\\\exists y:\\\\exists x:p(x,y)\\\\\\\\\\nlogseq____&amp;[\\\\forall x_1:\\\\forall x_2: \\\\cdots:\\\\forall x_n:p(x_1,x_2,\\\\cdots,x_n)\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\equiv\\\\forall_{x_{\\\\pi(1)}}:\\\\forall_{x_{\\\\pi(1)}}:\\\\cdots:\\\\forall_{x_{\\\\pi(1)}}:p(x_1,x_2,\\\\cdots,x_n)\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Flogseq____&quot;,259,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Vlogseq____&quot;,259,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-f410-4139-9825-09e6a8df9681logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Widerspruch = ↯, #logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Flogseq____&quot;,271,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Vlogseq____&quot;,271,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-fa11-4c5f-888c-2b0cfaba2ec0logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Wäre $y$ aus $\\\\Reals$ mit $xlogseq____&lt;y$ für alle $x$ aus $\\\\Reals$, so insbesondere auch $ylogseq____&lt;y$, Widerspruch. $\\\\blacksquare$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Flogseq____&quot;,264,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Vlogseq____&quot;,264,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-30cc-4cf4-bf89-bdfc60ef9333logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\exists x:p(x)$ ist die Aussage: \\logseq____&quot;Es gibt (wenigstens) ein x aus U für das $p(x)$ wahr ist\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w \\\\quadlogseq____&amp;\\\\text{falls }p(x)\\\\text{ w ist für (wenigstens) ein x aus U}\\\\\\\\f\\\\quad logseq____&amp;\\\\text{falls }p(x)\\\\text{ f ist für alle x aus U}\\\\end{cases}$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Flogseq____&quot;,254,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Vlogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Ulogseq____&quot;,166,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Hlogseq____&quot;,166,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-a95f-4902-9316-606e27830ddflogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Schachtelung von quantoren 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logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870929]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Jlogseq____&quot;,[],536870929]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^17logseq____&quot;,false,536870929]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-ebd4-491d-b5c4-4544f0cb3bc1logseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Bei [[Multiplikation]] oder [[Division]] mit einer negativen Zahl wird das [[Ungleichheitszeichen]] umgekehrtlogseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Flogseq____&quot;,305,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Xlogseq____&quot;,108,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Vlogseq____&quot;,305,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,108,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,302,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,303,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,304,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Hlogseq____&quot;,302,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Hlogseq____&quot;,303,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Hlogseq____&quot;,304,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^17logseq____&quot;,true,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-3fa4-40d5-9b5c-57961deb0baalogseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\logseq____&quot;logseq____&gt;\\logseq____&quot;logseq____&amp;\\\\rightarrow\\logseq____&quot;logseq____&lt;\\logseq____&quot;\\\\\\\\\\n\\logseq____&quot;logseq____&lt;\\logseq____&quot;logseq____&amp;\\\\rightarrow\\logseq____&quot;logseq____&gt;\\logseq____&quot;\\\\\\\\\\n\\logseq____&quot;\\\\ge\\logseq____&quot;logseq____&amp;\\\\rightarrow\\logseq____&quot;\\\\le\\logseq____&quot;\\\\\\\\\\n\\logseq____&quot;\\\\le\\logseq____&quot;logseq____&amp;\\\\rightarrow\\logseq____&quot;\\\\ge\\logseq____&quot;\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Flogseq____&quot;,306,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Xlogseq____&quot;,108,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Vlogseq____&quot;,306,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,108,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,302,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,303,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,304,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^17logseq____&quot;,true,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-70c1-4a6b-869d-f95ee9d52ea5logseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;logseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Flogseq____&quot;,307,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Xlogseq____&quot;,108,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Vlogseq____&quot;,306,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,108,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,302,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,303,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,304,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^17logseq____&quot;,true,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-bf99-447d-a547-ba5fa7e68fdelogseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Klogseq____&quot;,1697218324562,536870930]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^@logseq____&quot;,false,536870930]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;vorlesungs notizenlogseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^11logseq____&quot;,logseq____&quot;Vorlesungs Notizenlogseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Blogseq____&quot;,1697218324562,536870930]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-f463-42a1-b626-02fdb571dc54logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Auffrischung Mathematik]]logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Flogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Xlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Vlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,23,536870930]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Hlogseq____&quot;,23,536870930]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^17logseq____&quot;,true,536870930]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-9576-4ef7-b3e4-51015d40a6aalogseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;drawings are located in logseq____&lt;vault pathlogseq____&gt;/drawslogseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Flogseq____&quot;,325,536870930]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Xlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Vlogseq____&quot;,325,536870930]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^17logseq____&quot;,true,536870930]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-9431-4686-a1c8-74f4af27f54flogseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;logseq____&lt;h1 style=\\logseq____&quot;color: red;\\logseq____&quot;logseq____&gt;Some drawings were not loadedlogseq____&lt;/h1logseq____&gt;logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Flogseq____&quot;,323,536870930]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Xlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Vlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^17logseq____&quot;,true,536870930]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-810e-45d4-99f4-85f564cfaa97logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## The svgs for following drawing are missinglogseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Flogseq____&quot;,325,536870930]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Xlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Vlogseq____&quot;,313,536870930]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870930]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Jlogseq____&quot;,[],536870930]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^17logseq____&quot;,true,536870930]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-f9e0-4a12-8b86-e2b95e7264eelogseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Rename the file so the base names 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themelogseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Flogseq____&quot;,324,536870930]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Xlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Vlogseq____&quot;,324,536870930]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ulogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^17logseq____&quot;,true,536870930]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-1775-4ed5-9fe0-41e6f5781b35logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;each \\logseq____&quot;.excalidraw\\logseq____&quot; drawing file should have an equivalent \\logseq____&quot;.svg\\logseq____&quot; file in logseq____&lt;vault pathlogseq____&gt;/assets/excalidraw_svg with the same basenamelogseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Flogseq____&quot;,312,536870930]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Xlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Vlogseq____&quot;,325,536870930]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Ulogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^17logseq____&quot;,true,536870930]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-4235-490d-9cbb-b1d4d7b869calogseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Mathematik für Informatiker 1]]logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Flogseq____&quot;,311,536870930]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Xlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Vlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,279,536870930]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Hlogseq____&quot;,279,536870930]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^17logseq____&quot;,true,536870930]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-fd2f-4c34-b726-ad497b30afc4logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Grundlagen und Diskrete Strukturen]]logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Flogseq____&quot;,318,536870930]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Xlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Vlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ulogseq____&quot;,158,536870930]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ulogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Hlogseq____&quot;,158,536870930]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^17logseq____&quot;,true,536870930]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-101d-4b77-92df-fbc7834a94aelogseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### Example\\n```\\nlogseq____&lt;vault pathlogseq____&gt;/draws/2023-10-08-21-23-31.excalidraw\\nlogseq____&lt;vault pathlogseq____&gt;/assets/excalidraw_svg/2023-10-08-21-23-31.svg\\n```logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Flogseq____&quot;,317,536870930]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Xlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Vlogseq____&quot;,325,536870930]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Ulogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870930]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Jlogseq____&quot;,[],536870930]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^17logseq____&quot;,true,536870930]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-aa75-4c39-880c-e7960eda73b5logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Click \\logseq____&quot;SVG\\logseq____&quot; and copy to logseq____&lt;vault 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und 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create a missing svg file, head to https://excalidraw.com/, paste the .excalidraw file, Click the Hamburger Menu logseq____&gt; Export Imagelogseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Flogseq____&quot;,320,536870930]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Xlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Vlogseq____&quot;,325,536870930]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Ulogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^17logseq____&quot;,true,536870930]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297f14-be60-4d6a-a33e-d438ef9c4448logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## How to fix as a Contributorlogseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Flogseq____&quot;,313,536870930]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Xlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Vlogseq____&quot;,313,536870930]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ulogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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