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[[Binomische Formeln]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Flogseq____&quot;,80,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Vlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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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; 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logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Hlogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-5031-4c18-8010-2dbbe8edd7b7logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Herleitung mit }$[[Quadratische Ergänzung]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&amp;=0logseq____&amp;|logseq____&amp;-q\\\\\\\\\\nx^2+pxlogseq____&amp;=-qlogseq____&amp;|logseq____&amp;+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\nx^2+px+\\\\left(\\\\frac p2\\\\right)^2logseq____&amp;=-q+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\n\\\\underbrace{\\\\left(x+\\\\frac 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p2\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Flogseq____&quot;,135,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Vlogseq____&quot;,135,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Ulogseq____&quot;,59,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Ulogseq____&quot;,62,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Ulogseq____&quot;,76,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Hlogseq____&quot;,59,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-f204-4d1d-9b5c-1478fb51edb6logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nax^2+bx+clogseq____&amp;=0logseq____&amp;|:a\\\\quadlogseq____&amp;a\\\\ne0\\\\\\\\\\nx^2+\\\\frac ba x + \\\\frac ca logseq____&amp;= 0\\\\\\\\\\nplogseq____&amp;=\\\\frac ba,logseq____&amp;q = \\\\frac ca\\\\\\\\\\nx^2+px+qlogseq____&amp;=0\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Flogseq____&quot;,128,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Vlogseq____&quot;,128,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ulogseq____&quot;,62,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-b441-4510-b31c-b5adc5ea29b4logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[111,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;,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Flogseq____&quot;,84,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Vlogseq____&quot;,84,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-3085-4d23-af9d-481418844972logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Potenzen]] und [[Wurzeln]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Flogseq____&quot;,87,536870921]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Vlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Hlogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Hlogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-1d2a-4d32-9845-5e026437aeaflogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[113,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;, 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x\\\\ne0\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Flogseq____&quot;,115,536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Vlogseq____&quot;,80,536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Ulogseq____&quot;,69,536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-585b-470a-8875-4aee0848dc36logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^Flogseq____&quot;,113,536870921]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^Vlogseq____&quot;,113,536870921]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^Ulogseq____&quot;,69,536870921]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^Ulogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^Hlogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-ff2a-4d90-a201-d1ac5a4b095elogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[115,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;,536870921]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Flogseq____&quot;,80,536870921]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Vlogseq____&quot;,80,536870921]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Ulogseq____&quot;,69,536870921]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-9f69-4f7b-ac7a-a7071ef69f18logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Satz von Vieta]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&amp;=0 logseq____&amp;logseq____&amp; \\\\text{habe }x_{1,2}\\\\text{ als Lösung}\\\\\\\\\\nx_1+x_2logseq____&amp;=-p logseq____&amp;logseq____&amp; x_1*x_2=q\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Flogseq____&quot;,109,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Vlogseq____&quot;,135,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Ulogseq____&quot;,62,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Ulogseq____&quot;,74,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Ulogseq____&quot;,76,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Hlogseq____&quot;,74,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-11e2-4f5e-9e07-cbbadd4f10adlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[117,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;,536870921]],[logseq____&quot;^15logseq____&quot;,[117,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[117,logseq____&quot;^Flogseq____&quot;,102,536870921]],[logseq____&quot;^15logseq____&quot;,[117,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[117,logseq____&quot;^Vlogseq____&quot;,102,536870921]],[logseq____&quot;^15logseq____&quot;,[117,logseq____&quot;^Ulogseq____&quot;,64,536870921]],[logseq____&quot;^15logseq____&quot;,[117,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[117,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[117,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-6e4b-4f8f-9584-9ed826990933logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Allgemein}$\\n\\\\begin{align}\\n|y|logseq____&amp;=\\\\begin{cases}\\ny logseq____&amp;\\\\text{ falls } y\\\\ge0\\\\\\\\\\n-y logseq____&amp;\\\\text{ falls } ylogseq____&lt;0\\\\\\\\\\n\\\\end{cases}\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Flogseq____&quot;,89,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Vlogseq____&quot;,125,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-e599-44e3-8717-04d5cf98246blogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Allgemein}$\\n\\\\begin{align}\\n\\\\ln a + \\\\ln b logseq____&amp;= \\\\ln(a*b) \\\\\\\\\\n\\\\ln(-a) logseq____&amp;= \\\\frac1{\\\\ln 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} x=\\\\frac25 \\\\text{ und } y=\\\\frac37 \\\\text{ ist }\\\\frac xy$\\n\\\\begin{align}\\n\\\\frac xy = \\\\frac{\\\\frac25}{\\\\frac37} = \\\\frac{2*7}{3*5}=\\\\frac{14}{15}\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Flogseq____&quot;,88,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Vlogseq____&quot;,88,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-2793-4d81-921d-e5fc17a69c83logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Häufige Falle:}$\\n\\\\begin{align}\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&amp;=(-1)^\\\\frac22logseq____&amp;=(-1)^1logseq____&amp;=-1\\\\\\\\\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&amp;=1^\\\\frac12logseq____&amp;logseq____&amp;=1\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Flogseq____&quot;,111,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Vlogseq____&quot;,84,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-a95e-486c-ac30-8dab81506f27logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Flogseq____&quot;,95,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Vlogseq____&quot;,107,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,61,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Hlogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-3b09-47ca-a2fa-ffe6452110ealogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Wurzelgleichung]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Flogseq____&quot;,128,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Vlogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,63,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Wurzeln]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Flogseq____&quot;,108,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Vlogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Hlogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-74b4-4e8e-b6f3-623bab3c656blogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[126,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;,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Flogseq____&quot;,125,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Vlogseq____&quot;,125,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Hlogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-1d66-48dc-b307-f0f19e28e1d0logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])\\n\\\\begin{align}\\nx^4-34x^2+225logseq____&amp;=0\\\\\\\\\\n\\\\text{substituiert }ylogseq____&amp;=x^2\\\\\\\\\\ny^2-34y+225logseq____&amp;=0\\\\\\\\\\ny_{1,2}logseq____&amp;=17\\\\pm\\\\sqrt{(-17)^2-225}\\\\\\\\\\nlogseq____&amp;=17\\\\pm\\\\sqrt{289-225}\\nlogseq____&amp;=17\\\\pm\\\\sqrt{64}=17\\\\pm8\\\\\\\\\\nlogseq____&amp;=\\\\left.\\\\begin{cases}\\n25\\\\\\\\\\n9\\n\\\\end{cases}\\\\right|\\\\begin{array}{l}\\nx^2=25logseq____&amp;\\\\rightarrow logseq____&amp;x_1=5;logseq____&amp;x_2=-5\\\\\\\\\\nx^2=9logseq____&amp;\\\\rightarrow logseq____&amp;x_1=3;logseq____&amp;x_2=-3\\\\\\\\\\n\\\\end{array}\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Flogseq____&quot;,116,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Vlogseq____&quot;,135,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,62,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,76,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Hlogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-82d4-42ee-90f8-e327a5eef7c1logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Quadratische Gleichungen]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Flogseq____&quot;,125,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Vlogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,62,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Hlogseq____&quot;,62,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-418e-476c-81a9-e2ddc4a10373logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\na^nlogseq____&amp;=\\\\underbrace{a*a*\\\\cdots*n}_n logseq____&amp; a,blogseq____&gt;0\\\\\\\\\\na^2b^2logseq____&amp;=(ab)^n\\\\\\\\\\n\\\\frac{a^n}{b^n}logseq____&amp;=\\\\left(\\\\frac ab\\\\right)^n\\\\\\\\\\na^na^mlogseq____&amp;=a^{n+m}\\\\\\\\\\n\\\\frac1{a^n}logseq____&amp;=a^{-n}\\\\\\\\\\n(a^n)^mlogseq____&amp;=a^{nm}\\\\\\\\\\na^0logseq____&amp;=1\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Flogseq____&quot;,108,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Vlogseq____&quot;,108,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-5313-4e1d-b77b-478d3a534eb2logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Flogseq____&quot;,92,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Vlogseq____&quot;,122,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,61,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Hlogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-9b62-49a0-bad5-283b80338deblogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____&gt;0$ welche keinen Sinn ergibtlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Flogseq____&quot;,86,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Vlogseq____&quot;,89,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Hlogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-58c7-4a53-abe7-2be6f8333fa7logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten 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an [Punkten]([[Punkte]]) $(x,y)$ der [Ebene]([[Ebenen]]) bei denen die [[Summe]] der [Abstände]([[Abstand]]) der Punkte zu zwei [festen Punkten]([[Fester Punkt]]) $F_1,F_2$ ([Brennpunkte]([[Brennpunkt]])) [[konstant]] 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Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Flogseq____&quot;,161,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Xlogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Vlogseq____&quot;,161,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Hlogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-3982-48e9-ba30-d060bb53fc25logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Punkt}(a,0)$\\n\\\\begin{align}\\nl_1logseq____&amp;=a+e\\\\\\\\\\nl_2logseq____&amp;=a-e\\\\\\\\\\nllogseq____&amp;=2a,\\\\quad a=\\\\frac l2\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Flogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Xlogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Vlogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ulogseq____&quot;,143,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ulogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-ad64-4e47-86b8-66b696728749logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[210,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;,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Flogseq____&quot;,216,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Xlogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Vlogseq____&quot;,208,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-998a-4670-ad9a-9f34d7d320a5logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 1}\\\\quad xlogseq____&lt;3$\\n\\\\begin{align}\\n|x-3|logseq____&amp;=-x+3\\\\\\\\\\n-x+3logseq____&amp;logseq____&lt;5 logseq____&amp;|logseq____&amp;-3\\\\\\\\\\n-xlogseq____&amp;logseq____&lt;2 logseq____&amp;|logseq____&amp;*-1\\\\\\\\\\nxlogseq____&amp;logseq____&gt;-2\\\\\\\\\\nL_1logseq____&amp;=(-2,3)\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Flogseq____&quot;,206,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Xlogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Vlogseq____&quot;,206,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-c396-42b8-8374-60b91f639cbalogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 2b}\\\\quad xlogseq____&lt;-2$\\n\\\\begin{align}\\n|\\\\underbrace{x+2}_{logseq____&lt;0}logseq____&amp;=-(x+2)=-x-2\\\\\\\\\\n-x+3logseq____&amp;\\\\le -x-2 logseq____&amp;|logseq____&amp;+x\\\\\\\\\\n3logseq____&amp;\\\\le-2logseq____&amp;logseq____&amp;\\\\underset{falsche Aussage}{f.A}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Flogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Xlogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Vlogseq____&quot;,215,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-4079-4ef2-8d86-cffe47163a0elogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[213,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 interval}\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Flogseq____&quot;,193,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Xlogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Vlogseq____&quot;,169,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ulogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ulogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-dbef-4b29-9ebd-f052ad51cd8dlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 2}\\\\quad xlogseq____&lt;3$\\n\\\\begin{align}\\n|\\\\underbrace{x-3}_{logseq____&lt;0}|logseq____&amp;=6(x-3)=-x+3\\\\\\\\\\n-x+3logseq____&amp;\\\\le|x+2|\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Flogseq____&quot;,163,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Xlogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Vlogseq____&quot;,215,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-d50f-462b-9cbb-a903c2d58c87logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Flogseq____&quot;,201,536870922]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Xlogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Vlogseq____&quot;,201,536870922]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ulogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ulogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ulogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Hlogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-632f-493f-979a-0afee351d66flogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 3}\\\\quad xlogseq____&gt;3$\\n\\\\begin{align}\\nx+5logseq____&amp;logseq____&gt;0\\\\\\\\\\n|x+5|logseq____&amp;=x+5\\\\\\\\\\nx-3logseq____&amp;\\\\ge0\\\\\\\\\\n|x-3|logseq____&amp;=x-3\\\\\\\\\\nx+5logseq____&amp;logseq____&lt;2(x-3)\\\\\\\\\\nx+5logseq____&amp;logseq____&lt;2x-3 logseq____&amp;|logseq____&amp; -2x-5\\\\\\\\\\n-xlogseq____&amp;logseq____&lt;-11 logseq____&amp;|logseq____&amp; *(-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;,536870922]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Flogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Xlogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Vlogseq____&quot;,208,536870922]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ulogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ulogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ulogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-6f5a-4e34-95ee-353acf8aab07logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Klogseq____&quot;,1697763818697,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;grundlagen 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}x,y,z\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nlogseq____&amp;x^n+y^n=z^n\\\\text{ eine Lösung}logseq____&amp;logseq____&amp; (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nlogseq____&amp;x,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp;\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Gott ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Nietzsche ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Flogseq____&quot;,251,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Vlogseq____&quot;,247,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-4108-44ca-9889-c1dc7147b29flogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Flogseq____&quot;,245,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Vlogseq____&quot;,245,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,222,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,225,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,226,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,233,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,240,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Hlogseq____&quot;,225,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Hlogseq____&quot;,226,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Hlogseq____&quot;,233,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Hlogseq____&quot;,240,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-8d13-4b36-aae1-065972e8b764logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussagenlogische Variable]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Flogseq____&quot;,258,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Vlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,223,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Hlogseq____&quot;,223,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-dacd-413a-85cd-7dc1693119b6logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;C. Meinel, M. Mundhenk, [[\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. Auflage 2011]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Flogseq____&quot;,257,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Vlogseq____&quot;,257,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,227,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Hlogseq____&quot;,227,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-1289-413d-887e-007f97163378logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Flogseq____&quot;,248,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Vlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,222,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Hlogseq____&quot;,222,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Hlogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-9b49-482a-b283-30f8de45402blogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $w$ istlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Flogseq____&quot;,260,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Vlogseq____&quot;,260,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,228,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-bdce-4e52-946e-2bbab7304fe0logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 1. [[Aussagen]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Flogseq____&quot;,257,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Vlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Hlogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-cb6a-42ac-9f0f-3489746160d1logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Belegung]] (der [[Variablen]])logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Flogseq____&quot;,250,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Vlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,230,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,240,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Hlogseq____&quot;,230,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Hlogseq____&quot;,240,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-6d03-49d8-9a6b-ae2f191e9f7alogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formeln $p,q$ [logisch äquivalent]([[Logisch Äquivalent]]), wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Flogseq____&quot;,253,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Vlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,222,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,232,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Hlogseq____&quot;,222,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Hlogseq____&quot;,232,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Hlogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-7740-48ab-8038-bf548b911877logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussageformel]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Flogseq____&quot;,243,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Vlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Hlogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-90a5-4bbc-a33d-ff14f8cd2b9dlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Satz, der wahr oder falsch ist, d.h. der [[Wahrheitswert]] $w$ bzw $f$ hat ($t/f$, $1/0$, $\\\\text{wahr}/\\\\text{falsch}$)logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Flogseq____&quot;,247,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Vlogseq____&quot;,247,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,226,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Hlogseq____&quot;,226,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-aa25-4e81-a97a-096d8e03c196logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[252,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Flogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Vlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Hlogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-cdb5-438f-a958-86fd84529548logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Kontradiktion]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Flogseq____&quot;,260,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Vlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,229,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Hlogseq____&quot;,229,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-8580-4e56-846d-fd5a3b7fe4b5logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $f$ istlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Flogseq____&quot;,253,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Vlogseq____&quot;,253,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,229,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-f119-462d-8049-03880efa55e3logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n(p\\\\rightarrow q)logseq____&amp;\\\\equiv((\\\\neg q)\\\\rightarrow(\\\\neg p))\\\\\\\\\\n(p\\\\land(p\\\\rightarrow q)) logseq____&amp;\\\\rightarrow q logseq____&amp;\\\\quad \\\\text{Tantologie}\\n\\\\end{align}logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Flogseq____&quot;,259,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Vlogseq____&quot;,259,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,68,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-9367-4411-b2b7-99a496d80c4alogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel: Bestimmung des }$[[Wahrheitswerteverlauf]]$\\\\text{ von }(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)$\\n|$p$|$q$||$p\\\\rightarrow q$|$q\\\\rightarrow p$|$(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)|$p\\\\leftrightarrow q$|\\n|-|-|-|-|-|-|\\n|f|f||w|w|w|w|\\n|f|w||w|f|f|f|\\n|w|f||f|w|f|f|\\n|w|w||w|w|w|w|logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Flogseq____&quot;,242,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Vlogseq____&quot;,245,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,222,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Hlogseq____&quot;,222,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-a142-4c14-abe5-510efaf880b1logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Büchertiplogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Flogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Vlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^17logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-db42-49e2-a133-f204e2a78e8flogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[258,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Flogseq____&quot;,266,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Vlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,226,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,231,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,233,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,237,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Hlogseq____&quot;,226,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Hlogseq____&quot;,231,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Hlogseq____&quot;,233,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Hlogseq____&quot;,237,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-361a-4519-8d1c-185874950fe6logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Weitere [[Beispiele]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Flogseq____&quot;,267,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Vlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,68,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Hlogseq____&quot;,68,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-1b60-4214-a456-f3e6093d8328logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Tantologie]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Flogseq____&quot;,245,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Vlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,228,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Hlogseq____&quot;,228,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-733e-4e4e-9b5c-ef4718fc0332logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Zuordnung von $w/f$ an jede [Variable]([[Variablen]]) einer [[Aussageformel]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Flogseq____&quot;,248,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Vlogseq____&quot;,248,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,230,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,240,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Hlogseq____&quot;,230,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Hlogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-b03b-4f21-b4cc-59de8f278f3elogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\np\\\\land q\\\\lor r\\\\\\\\\\n(p\\\\land q)\\\\lor r\\\\\\\\\\np\\\\land (q\\\\lor r)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Flogseq____&quot;,266,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Vlogseq____&quot;,266,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,68,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-16a7-4f81-a9e0-aee2f0d03ad0logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Variable]([[Variablen]]), die den Wert $w$ oder $f$ annimmtlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Flogseq____&quot;,243,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Vlogseq____&quot;,243,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,223,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,230,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Hlogseq____&quot;,230,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-258e-4a3e-927d-f3f32f730028logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt 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beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der [[Aussagenlogik]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Flogseq____&quot;,321,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Vlogseq____&quot;,296,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,274,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,293,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Hlogseq____&quot;,274,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Hlogseq____&quot;,293,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-54c4-4369-883e-6dc257ee6ecclogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\logseq____&quot;\\\\text{x ist prim}\\logseq____&quot; \\\\quad logseq____&amp; \\\\text{ist AF mit Variablen x über den natürlichen Zahlen}\\\\\\\\\\n\\logseq____&quot;\\\\underbrace{x}_{x_1}logseq____&lt;\\\\underbrace{y}_{x_2}\\logseq____&quot;\\\\quad logseq____&amp;\\\\text{ist AF mit Variablen }x,y\\\\text{ über die reellen Zahlen } \\\\underbrace{\\\\Reals}_{U_1},\\\\underbrace{\\\\Reals}_{U_2}\\\\\\\\\\n\\logseq____&quot;\\\\text{x ist wahr}\\logseq____&quot;\\\\quadlogseq____&amp;\\\\text{ist AF mit Variablen x über dem Universum der Aussagen}\\n\\\\end{align}logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Flogseq____&quot;,314,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Vlogseq____&quot;,296,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-8ad0-4cbb-a138-3b6ea550b747logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche Regeln]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Flogseq____&quot;,298,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Vlogseq____&quot;,298,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,271,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,276,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,279,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,280,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,286,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,287,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Hlogseq____&quot;,271,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Hlogseq____&quot;,276,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Hlogseq____&quot;,279,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Hlogseq____&quot;,280,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Hlogseq____&quot;,286,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Hlogseq____&quot;,287,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-85ee-40e8-90a1-8345a399c3a0logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[303,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;,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Flogseq____&quot;,312,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Vlogseq____&quot;,312,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-e5b0-4229-878a-55809594c216logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[304,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;,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Flogseq____&quot;,315,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Vlogseq____&quot;,315,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,272,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,275,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Hlogseq____&quot;,272,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Hlogseq____&quot;,275,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-456f-4c26-952e-27455123d8edlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[305,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;,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Flogseq____&quot;,316,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Vlogseq____&quot;,316,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-5aa0-43e3-b54c-e56348f3b467logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Schachtelung von quantoren ([Beispiel]([[Beispiele]])):logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Flogseq____&quot;,305,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Vlogseq____&quot;,316,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Hlogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-81bd-4d32-94f0-7718b4eb14felogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[307,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;,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Flogseq____&quot;,301,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Vlogseq____&quot;,301,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-e808-45ab-98c8-345073c7f04elogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Regeln]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Flogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Vlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Jlogseq____&quot;,[],536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Hlogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^17logseq____&quot;,false,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-def5-4c2a-87d1-7065dde1ccd1logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Widerspruch = ↯, #logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Flogseq____&quot;,319,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Vlogseq____&quot;,319,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-97d5-4c92-ab68-5385787137c6logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Flogseq____&quot;,323,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Vlogseq____&quot;,299,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Hlogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-c46b-4861-82ab-1740f5daabc7logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Allquantor]] [[Existenzquantor]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Flogseq____&quot;,317,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Vlogseq____&quot;,317,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,283,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Hlogseq____&quot;,283,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Hlogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-66c0-4dc9-adb8-b0330fdd56f5logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Flogseq____&quot;,299,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Vlogseq____&quot;,296,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Hlogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-d6e7-435a-a994-3b3406fdf761logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Verschiedene [[Quantoren]] dürfen **nicht** vertauscht werdenlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Flogseq____&quot;,322,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Vlogseq____&quot;,323,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Hlogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-c355-4d1b-b5f9-804058667ca7logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Flogseq____&quot;,327,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Vlogseq____&quot;,296,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Hlogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-0542-4f84-906e-151a303c8700logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[315,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;,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Flogseq____&quot;,329,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Vlogseq____&quot;,329,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-bde8-4cd0-8544-abbde2bae7f6logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Regeln]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Flogseq____&quot;,324,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Vlogseq____&quot;,296,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ulogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,2],536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Jlogseq____&quot;,[],536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Hlogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-98e6-41e6-8788-4a0576de76b0logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\underbrace{\\\\forall}_\\\\text{Allquantor} x: p(x) logseq____&amp;\\\\equiv p(O_1) \\\\land p(O_2) \\\\land \\\\cdots \\\\land p(O_m)\\\\\\\\\\n\\\\underbrace{\\\\exists}_\\\\text{Existenzquantor} x: p(x) logseq____&amp;\\\\equiv p(0_1) \\\\lor p(O_2) \\\\lor \\\\cdots \\\\lor p(0_m)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Flogseq____&quot;,331,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Vlogseq____&quot;,296,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-f614-4101-8dd5-aa906dbca1fclogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Betrachte $\\logseq____&quot;xlogseq____&lt;y\\logseq____&quot;$ als AF über $\\\\Reals, \\\\Reals$logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Flogseq____&quot;,310,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Vlogseq____&quot;,310,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-5497-45c6-87ef-184cd67d18c7logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[319,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;,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Flogseq____&quot;,332,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Vlogseq____&quot;,332,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ulogseq____&quot;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-2761-4e8f-ba3b-a2ed18e7581flogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Flogseq____&quot;,305,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Vlogseq____&quot;,305,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Ulogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Ulogseq____&quot;,273,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Ulogseq____&quot;,285,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Ulogseq____&quot;,290,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Hlogseq____&quot;,273,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Hlogseq____&quot;,285,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Hlogseq____&quot;,290,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-c698-45ee-9bde-ef5e5cc81eb9logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x)$ AF in der Variablen $x$ über $U$:logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Flogseq____&quot;,301,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Vlogseq____&quot;,296,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-fe14-4c08-b96c-3cf2e983750dlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;wobei $\\\\pi$ eine \\logseq____&quot;[[Permutation]]\\logseq____&quot; der Zahl $(1,2,\\\\cdots,n)$ istlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Flogseq____&quot;,323,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Vlogseq____&quot;,323,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ulogseq____&quot;,284,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Hlogseq____&quot;,284,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-1e51-42d1-852b-c7ccbb14eec8logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[323,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;,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Flogseq____&quot;,299,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Vlogseq____&quot;,299,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-53e4-42e6-90e8-1109fa467b9flogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[324,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;,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Flogseq____&quot;,325,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Vlogseq____&quot;,296,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-e1cb-40c9-b6a2-5aebe093b942logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[325,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;,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Flogseq____&quot;,317,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Vlogseq____&quot;,296,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ulogseq____&quot;,226,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Hlogseq____&quot;,226,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-caaa-42b4-99c8-ca30c74943aclogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[326,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;,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Flogseq____&quot;,300,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Vlogseq____&quot;,296,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-7c54-4a0e-9cec-916f3d5ff328logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Satz]] mit [[Variablen]] $x_1,\\\\cdots,x_n$, der bei Ersetzung jedes $x_j$ durch ein [Objekt]([[Objekt (Logik)]]) aus $U_j$ stets zu einer [Aussage]([[Aussagen]]) wirdlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Flogseq____&quot;,297,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Vlogseq____&quot;,296,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Ulogseq____&quot;,230,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Ulogseq____&quot;,234,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Ulogseq____&quot;,291,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Ulogseq____&quot;,294,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Hlogseq____&quot;,230,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Hlogseq____&quot;,234,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Hlogseq____&quot;,291,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Hlogseq____&quot;,294,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-5365-4ec1-8b3d-2c9f67dad6b8logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[328,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 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x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist wahr}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^Flogseq____&quot;,318,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^Vlogseq____&quot;,318,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^Ulogseq____&quot;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^Hlogseq____&quot;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-e786-4d37-af71-940a9a937c95logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[330,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;,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^Flogseq____&quot;,321,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^Vlogseq____&quot;,321,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^Ulogseq____&quot;,226,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^Ulogseq____&quot;,234,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^Hlogseq____&quot;,226,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^Hlogseq____&quot;,234,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-1002-467b-b52b-d62baffe6239logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Endliches Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^Flogseq____&quot;,326,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^Vlogseq____&quot;,296,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531d1ea-a994-42de-8114-21d6df1ee633logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[332,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist 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