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gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____&gt;0$ welche keinen Sinn ergibtlogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Flogseq____&quot;,127,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Vlogseq____&quot;,83,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,59,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,67,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,69,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,74,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Hlogseq____&quot;,74,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dc-458d-4fea-96f5-0cf6271804b4logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Wurzeln]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Flogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Vlogseq____&quot;,131,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,59,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,69,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Jlogseq____&quot;,[],536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Hlogseq____&quot;,69,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dc-2f4b-4512-834a-5cc1c0719c16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Wenn }alogseq____&gt;0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac b{\\\\sqrt a} = \\\\frac b{\\\\sqrt a}*\\\\frac{\\\\sqrt a}{\\\\sqrt a} = \\\\frac {b\\\\sqrt a}a\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Flogseq____&quot;,103,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Vlogseq____&quot;,103,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,59,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,69,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,71,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,77,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dc-ebe9-4d2f-bc48-56e045ef3b60logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{array}{c} (a+b)^0logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;1 \\\\\\\\\\n(a+b)^1logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;1 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^2logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 2 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^3logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;1 logseq____&amp;logseq____&amp; 3 logseq____&amp;logseq____&amp; 3 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^4logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 4 logseq____&amp;logseq____&amp; 6 logseq____&amp;logseq____&amp; 4 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^5logseq____&amp;logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 5 logseq____&amp;logseq____&amp; 10 logseq____&amp;logseq____&amp; 10 logseq____&amp;logseq____&amp; 5 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^6logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 6 logseq____&amp;logseq____&amp; 15 logseq____&amp;logseq____&amp; 20 logseq____&amp;logseq____&amp; 15 logseq____&amp;logseq____&amp; 6 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^7logseq____&amp;1 logseq____&amp;logseq____&amp; 7 logseq____&amp;logseq____&amp;21 logseq____&amp;logseq____&amp; 35 logseq____&amp;logseq____&amp; 35 logseq____&amp;logseq____&amp; \\\\cdots\\\\end{array}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Flogseq____&quot;,118,536870920]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Vlogseq____&quot;,118,536870920]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,60,536870920]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,66,536870920]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dc-66df-4c7d-a18c-612e78ddfdd3logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Herleitung mit }$[[Quadratische Ergänzung]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&amp;=0logseq____&amp;|logseq____&amp;-q\\\\\\\\\\nx^2+pxlogseq____&amp;=-qlogseq____&amp;|logseq____&amp;+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\nx^2+px+\\\\left(\\\\frac p2\\\\right)^2logseq____&amp;=-q+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\n\\\\underbrace{\\\\left(x+\\\\frac p2\\\\right)^2}_\\\\text{1. binomische Formel}logseq____&amp;=-q+\\\\left(\\\\frac p2\\\\right)^2logseq____&amp;|logseq____&amp;\\\\sqrt{()}\\\\\\\\\\n\\\\left|x+\\\\frac p2\\\\right|logseq____&amp;=\\\\sqrt{\\\\frac{p^2}4-q}logseq____&amp;,logseq____&amp;\\\\text{ falls }\\\\frac{p^2}4-q\\\\ge0\\\\\\\\\\nx+\\\\frac p2logseq____&amp;=\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}logseq____&amp;|logseq____&amp;-\\\\frac p2\\\\\\\\\\nxlogseq____&amp;=-\\\\frac p2\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Flogseq____&quot;,116,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Vlogseq____&quot;,116,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,58,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,59,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,61,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,69,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,75,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Hlogseq____&quot;,58,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dc-7089-4d31-896e-bfc4d5aea9f3logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel für die 3. Binomische Formel}$\\n\\\\begin{align}\\n\\\\frac{\\\\frac1{a-b}+\\\\frac1{a+b}}{\\\\frac1{a-b}-\\\\frac1{a+b}}\\nlogseq____&amp;=\\\\frac{\\\\frac{a+b+a-b}{(a+b)*(a-b)}}{\\\\frac{a+b-(a-b)}{(a+b)*(a-b)}}\\nlogseq____&amp;=\\\\frac{a+b+a-b}{a+b-a+b}\\nlogseq____&amp;=\\\\frac{2a}{2b}\\nlogseq____&amp;=\\\\frac ab\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Flogseq____&quot;,125,536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Vlogseq____&quot;,124,536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,66,536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dc-64bf-4ba3-aefa-699c2b8db4b6logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\underbrace{\\\\frac6{2+\\\\sqrt2}*\\\\frac{2-\\\\sqrt2}{2-\\\\sqrt2}\\n= \\\\frac{6(2-\\\\sqrt2)}{2^2-(\\\\sqrt2)^2}}_\\\\text{3. binomische Formel}\\nlogseq____&amp;=\\\\frac{6(2-\\\\sqrt2)}2=3(2-\\\\sqrt2)\\\\\\\\\\n\\\\frac{a-b}{\\\\sqrt a+\\\\sqrt b}logseq____&amp;=\\\\frac{a-b}{\\\\sqrt a + \\\\sqrt b}\\\\frac{\\\\sqrt a-\\\\sqrt b}{\\\\sqrt a-\\\\sqrt b}logseq____&amp;, a,b,logseq____&gt;0\\\\notag\\\\\\\\\\n=\\\\frac{(a-b)(\\\\sqrt a-\\\\sqrt b)}{(a-b)}logseq____&amp;=\\\\sqrt a\\\\sqrt b\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Flogseq____&quot;,98,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Vlogseq____&quot;,98,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,59,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,67,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,69,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,71,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,77,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dc-2662-40d7-80a8-b0ebb607b897logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\sqrt[n]{a^n}logseq____&amp;=1^\\\\frac nn=a^1=a\\\\\\\\\\n\\\\sqrt[n]{\\\\frac ab} logseq____&amp;= \\\\frac{\\\\sqrt[n]a}{\\\\sqrt[n]b}\\\\\\\\\\n\\\\left(\\\\sqrt[n]a\\\\right)^mlogseq____&amp;=a^\\\\frac mn\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Flogseq____&quot;,119,536870920]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Vlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,59,536870920]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,69,536870920]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dc-4e91-4e3b-8bd0-c3ea062da1e7logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n(a+b)^3(a^2+b^2)^3(a-b)^3logseq____&amp;=(a^2+b^2)^3\\\\left((a+b)(a-b)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=(a^2+b^2)^3(a^2-b^2)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=\\\\left((a^2+b^2)(a^2-b^2)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=(a^4-b^4)^3\\\\\\\\\\n\\\\frac{a-b}{(a+b)^{-1}}logseq____&amp;=(a-b)(a+b)\\\\notag\\\\\\\\\\nlogseq____&amp;=a^2-b^2\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Flogseq____&quot;,87,536870920]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Vlogseq____&quot;,87,536870920]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Ulogseq____&quot;,59,536870920]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Ulogseq____&quot;,67,536870920]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Ulogseq____&quot;,69,536870920]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dc-1fea-4a40-8517-8f08b3de904blogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Einsetzen, um zu überprüfen, ob man eine Fallunterscheidung 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[[Binomische Formeln]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Flogseq____&quot;,122,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Vlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,66,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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von [Punkten]([[Punkte]]) $(x,y)$ in der [Ebene]([[Ebenen]])  die den gleichen [[Abstand]] r ([[Radius]]) zu einem [festen Punkt]([[Fester Punkt]]) ([[Mittelpunkt]])logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Flogseq____&quot;,168,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Xlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Vlogseq____&quot;,168,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,138,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,139,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,140,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,143,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,153,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,154,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Hlogseq____&quot;,139,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Hlogseq____&quot;,140,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Hlogseq____&quot;,143,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Hlogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Hlogseq____&quot;,153,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Hlogseq____&quot;,154,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Hlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-714b-48d8-a6ac-9ca83e191d73logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;![draws/2023-10-18-17-15-11.excalidraw](https://raw.githubusercontent.com/Surferlul/IA-Logseq-Publish/external-assets/svg-assets/draws/2023-10-18-17-15-11.excalidraw.svg)logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Flogseq____&quot;,190,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Xlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Vlogseq____&quot;,168,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,138,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-d254-4f71-ae18-4378c81d81dclogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;![draws/2023-10-18-17-34-30.excalidraw](https://raw.githubusercontent.com/Surferlul/IA-Logseq-Publish/external-assets/svg-assets/draws/2023-10-18-17-34-30.excalidraw.svg)logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Flogseq____&quot;,200,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Xlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Vlogseq____&quot;,196,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,138,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,142,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-1cd5-4a71-9804-15366cba6410logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Mengen]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Flogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Xlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Vlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Hlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^17logseq____&quot;,false,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-df4b-45fa-88a5-55f1dea8f3belogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME incompletelogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Flogseq____&quot;,178,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Xlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Vlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,74,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Hlogseq____&quot;,74,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-2942-4770-a9e7-7d615353a787logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 1} \\\\quad xlogseq____&lt;-5$\\n\\\\begin{align}\\nx+5logseq____&amp;logseq____&lt;0\\\\\\\\\\n|x+5|logseq____&amp;=-(x+5)=-x-5\\\\\\\\\\nx-3logseq____&amp;logseq____&lt;0\\\\\\\\\\n|x-3|logseq____&amp;=-(x-3)=-x+3\\\\\\\\\\n-x-5logseq____&amp;logseq____&lt; 2(-x+3)\\\\\\\\\\n-x-5logseq____&amp;logseq____&lt;-2x+6 logseq____&amp;|logseq____&amp;+5+2x\\\\\\\\\\nxlogseq____&lt;11\\\\\\\\\\n\\\\end{align}\\n\\\\begin{align}\\nL_1=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|xlogseq____&lt;-5,x\\\\le11\\\\right\\\\}=(-\\\\infty,-5)\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Flogseq____&quot;,203,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Xlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Vlogseq____&quot;,203,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,141,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-c1a9-4e8c-a73e-08dc66010b9dlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;![draws/2023-10-13-18-01-25.excalidraw](https://raw.githubusercontent.com/Surferlul/IA-Logseq-Publish/external-assets/svg-assets/draws/2023-10-13-18-01-25.excalidraw.svg)logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Flogseq____&quot;,185,536870921]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Xlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Vlogseq____&quot;,184,536870921]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-d94f-4f8e-88b5-3ed11699f9c8logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[182,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;,536870921]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Flogseq____&quot;,157,536870921]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Xlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Vlogseq____&quot;,203,536870921]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,141,536870921]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-50bd-4ab2-a3d7-af145135db9blogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[183,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;,536870921]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Flogseq____&quot;,204,536870921]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Xlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Vlogseq____&quot;,170,536870921]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-a656-42a4-be49-050e08b96fa5logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;**oder** $\\\\rightarrow$ 5 ist abstand von x zu 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[[Fallunterscheidung]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Flogseq____&quot;,169,536870921]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Xlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Vlogseq____&quot;,169,536870921]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,141,536870921]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870921]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Hlogseq____&quot;,141,536870921]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-56bc-4b48-9859-afe4c311965alogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Kombinieren:\\n\\\\begin{align}\\nL=L_1\\\\cup L_2=(-2,8)\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Flogseq____&quot;,194,536870921]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Xlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Vlogseq____&quot;,197,536870921]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,141,536870921]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-0d9a-4700-8446-36d5402696balogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]\\n\\\\begin{align}\\n|5|=logseq____&amp;5\\\\\\\\\\n|-3,3|logseq____&amp;=3,3\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Flogseq____&quot;,193,536870921]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Xlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Vlogseq____&quot;,164,536870921]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Hlogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-597d-4196-a542-1d8dc83dabbalogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Menge]([[Mengen]]) 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]] istlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Flogseq____&quot;,196,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Xlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Vlogseq____&quot;,196,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,138,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,139,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,142,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,144,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,146,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,149,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,153,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,154,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Hlogseq____&quot;,139,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Hlogseq____&quot;,144,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Hlogseq____&quot;,146,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Hlogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Hlogseq____&quot;,149,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Hlogseq____&quot;,153,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Hlogseq____&quot;,154,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Hlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-5cc0-4607-91aa-23db39db1ed4logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Flogseq____&quot;,207,536870921]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Xlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Vlogseq____&quot;,207,536870921]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,141,536870921]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870921]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Hlogseq____&quot;,141,536870921]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-1faa-4085-966d-c0ff73b89853logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[202,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;,536870921]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Flogseq____&quot;,197,536870921]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Xlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Vlogseq____&quot;,197,536870921]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,141,536870921]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-f263-419c-bc95-c963988fdcf3logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Flogseq____&quot;,160,536870921]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Xlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Vlogseq____&quot;,160,536870921]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,141,536870921]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870921]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Hlogseq____&quot;,141,536870921]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-ca8e-4ec4-86e8-fe052fb3373clogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Menge aller reellen Zahlen zwischen 1 und 4 inklusive 1 und 4\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-1\\\\le x\\\\le4\\\\right\\\\}=:\\\\underbrace{[-1,4]}_\\\\text{Abgeschlossenes Interval}\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Flogseq____&quot;,170,536870921]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Xlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Vlogseq____&quot;,170,536870921]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-e762-416c-9ae0-03ad8de394c7logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Flogseq____&quot;,165,536870921]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Xlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Vlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-4485-4793-b9df-6d876f453c85logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 1}\\\\quad x\\\\ge3$\\n\\\\begin{align}\\n|x-3|logseq____&amp;=x-3\\\\\\\\\\nx-3\\\\le|x+2|\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Flogseq____&quot;,201,536870921]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Xlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Vlogseq____&quot;,201,536870921]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,141,536870921]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-f983-4c4b-a0c2-b1904406ec85logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$$L=\\\\left\\\\{\\\\underbrace{x\\\\in\\\\Reals}_{0\\\\notin L}\\\\:\\\\middle|\\\\:\\\\underbrace{|x-3|\\\\le|x+2}_{1\\\\in L}\\\\right\\\\}$$\\n$0\\\\notin L\\\\rightarrow\\\\text{0 steht nicht in Lösungsmenge}$\\n$1\\\\in L\\\\rightarrow\\\\text{1 gehört zu 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[[Wahrheitswerteverlauf]] einer 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logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Hlogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Hlogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-315f-4c9b-8a02-09c17e054ecflogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $w$ istlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Flogseq____&quot;,246,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Vlogseq____&quot;,246,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Ulogseq____&quot;,219,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-9903-41ca-a033-dc68796ab402logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;C. Meinel, M. Mundhenk,  [[\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. Auflage 2011]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Flogseq____&quot;,236,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Vlogseq____&quot;,236,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Hlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-9772-4001-869b-3619f9d6ba2alogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussagenlogische Variable]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Flogseq____&quot;,259,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Vlogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Ulogseq____&quot;,214,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Hlogseq____&quot;,214,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-968c-4cf1-920b-ba763705bfaflogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Büchertiplogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Flogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Vlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^17logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-e2de-424d-baeb-c22e18afa2f9logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[237,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;,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Flogseq____&quot;,239,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Vlogseq____&quot;,239,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Hlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-e0a5-459f-9571-dcc9f5811199logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Weitere [[Beispiele]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Flogseq____&quot;,252,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Vlogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,67,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Hlogseq____&quot;,67,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-fe01-44aa-8e9c-3aed2ac6fa23logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 1. [[Aussagen]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Flogseq____&quot;,236,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Vlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Hlogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-c71d-4051-86c4-a87e75c4e244logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\nlogseq____&amp;\\logseq____&quot;5\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;\\\\quadlogseq____&amp; (w)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;4\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;logseq____&amp; (f)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Jede gerade Zahl }\\\\ge4\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ ist Summe zweier Primzahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage, }w\\\\text{ oder }f)\\\\notag\\\\\\\\\\nlogseq____&amp;(\\\\text{Vermutung von Goldback 1742})\\\\text{, }logseq____&amp;logseq____&amp;\\\\text{richtig für gerade Zahlen bis }4*10^{18}\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Dieser Satz ist falsch}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{keine Aussage})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Gleichung } x^2+y^2=z^2 \\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ hat eine Lösung }x,y,z\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nlogseq____&amp;x^n+y^n=z^n\\\\text{ eine Lösung}logseq____&amp;logseq____&amp; (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nlogseq____&amp;x,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp;\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Gott ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Nietzsche ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Flogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Vlogseq____&quot;,239,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-ac35-46f9-bb9f-18807c3f5097logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,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;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Flogseq____&quot;,238,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Vlogseq____&quot;,238,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,67,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-4adc-450b-b059-551f2d96628elogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Variable]([[Variablen]]), die den Wert $w$ oder $f$ annimmtlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Flogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Vlogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,214,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Hlogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-79ac-4158-b1f1-61303b07a5bflogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Flogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Vlogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,231,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Hlogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Hlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Hlogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Hlogseq____&quot;,231,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-0318-4f72-b8c2-8e85b491b6dflogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,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;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Flogseq____&quot;,243,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Vlogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Hlogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-b633-4150-aa2a-e61517d6b29flogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,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;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Flogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Vlogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,230,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Hlogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Hlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Hlogseq____&quot;,230,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-2091-4f5f-a3c1-a76147034cfclogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Tantologie]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Flogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Vlogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,219,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Hlogseq____&quot;,219,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-3a30-4b38-8700-07e4864adcc0logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Flogseq____&quot;,253,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Vlogseq____&quot;,253,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,74,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,226,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Hlogseq____&quot;,74,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Hlogseq____&quot;,226,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-b934-4359-8b3e-f66f65b88135logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[248,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;,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Flogseq____&quot;,250,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Vlogseq____&quot;,250,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,67,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-f0e1-4843-93cd-dfb185674598logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Kontradiktion]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Flogseq____&quot;,246,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Vlogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Hlogseq____&quot;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-d85d-4edf-bf1e-7a86033978a1logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Flogseq____&quot;,258,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Vlogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,67,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Hlogseq____&quot;,67,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-7e8a-4d38-bc9e-f40483cef240logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $f$ istlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Flogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Vlogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-2e8e-4d2d-988b-7a305288f652logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Flogseq____&quot;,245,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Vlogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,219,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Hlogseq____&quot;,219,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-ee72-4709-b021-e0d29b01947blogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussageformel]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Flogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Vlogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Hlogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-f268-42c2-b7e7-3935643b82dalogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wikipedia]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Flogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Vlogseq____&quot;,236,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,215,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Hlogseq____&quot;,215,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-852b-4050-8a19-7a6eb77e417blogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Zuordnung von $w/f$ an jede [Variable]([[Variablen]]) einer [[Aussageformel]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Flogseq____&quot;,256,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Vlogseq____&quot;,256,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,231,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Hlogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Hlogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-eebd-44e6-9d9f-5109a2e9810flogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Belegung]] (der [[Variablen]])logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Flogseq____&quot;,253,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Vlogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,231,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Hlogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Hlogseq____&quot;,231,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-9e11-406d-946b-9323daed031elogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Verknüpfung von Aussagen]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Flogseq____&quot;,240,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Vlogseq____&quot;,239,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,2],536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Hlogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-3be7-4758-a407-6893f7078444logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[258,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;,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Flogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Vlogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Hlogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-302b-468c-b4d7-62434beaba84logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[259,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;,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Flogseq____&quot;,250,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Xlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Vlogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Hlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Hlogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Hlogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Hlogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001dd-1284-48d0-9876-ea5bc56a27bblogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Klogseq____&quot;,1697645022224,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;regelnlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^11logseq____&quot;,logseq____&quot;Regelnlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Blogseq____&quot;,1697645022224,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-579c-4b59-8239-6b12cb047ae4logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Klogseq____&quot;,1697645022199,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;de morgansche regelnlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^11logseq____&quot;,logseq____&quot;de Morgansche Regelnlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Blogseq____&quot;,1697645022199,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-48f3-4df0-b0de-74f35944b8d3logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Klogseq____&quot;,1697645022243,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;q.e.d.logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^11logseq____&quot;,logseq____&quot;Q.E.D.logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Blogseq____&quot;,1697645022243,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-ef8e-4d99-b66c-0803168e1ed3logseq____&quot;,536870932]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Klogseq____&quot;,1697645022226,536870924]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;große de morgansche regelnlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^11logseq____&quot;,logseq____&quot;Große de Morgansche Regelnlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Blogseq____&quot;,1697645022226,536870924]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-a7b8-4149-a8a6-9bf14f7c5bb4logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Klogseq____&quot;,1697645022220,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;aussagenlogiklogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^11logseq____&quot;,logseq____&quot;Aussagenlogiklogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Blogseq____&quot;,1697645022220,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-ca46-419f-9b4e-cd6622cc1b13logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Klogseq____&quot;,1697645022242,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;w.z.b.w.logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^11logseq____&quot;,logseq____&quot;w.z.b.w.logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Blogseq____&quot;,1697645022242,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-20ae-4e85-949d-5fc1434711a2logseq____&quot;,536870932]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Klogseq____&quot;,1697645022204,536870924]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;kommutativlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^11logseq____&quot;,logseq____&quot;kommutativlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Blogseq____&quot;,1697645022204,536870924]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-0e4b-416c-83f0-1cbc350f9458logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Klogseq____&quot;,1697645022238,536870924]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;grundlagen und diskrete strukturen/23-10-13logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Alogseq____&quot;,209,536870924]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^11logseq____&quot;,logseq____&quot;Grundlagen und Diskrete 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p(x)\\\\quadlogseq____&amp;Kontradiktion\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[289,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[289,logseq____&quot;^Flogseq____&quot;,300,536870924]],[logseq____&quot;^15logseq____&quot;,[289,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[289,logseq____&quot;^Vlogseq____&quot;,313,536870924]],[logseq____&quot;^15logseq____&quot;,[289,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[289,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[289,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[289,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-4ad1-44d3-badb-91e77874e8dclogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[290,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[290,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[290,logseq____&quot;^Flogseq____&quot;,323,536870924]],[logseq____&quot;^15logseq____&quot;,[290,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[290,logseq____&quot;^Vlogseq____&quot;,313,536870924]],[logseq____&quot;^15logseq____&quot;,[290,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[290,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[290,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[290,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-876f-40fa-94aa-3c1b48493817logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[291,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x)$ AF in der Variablen $x$ über $U$:logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[291,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[291,logseq____&quot;^Flogseq____&quot;,288,536870924]],[logseq____&quot;^15logseq____&quot;,[291,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[291,logseq____&quot;^Vlogseq____&quot;,313,536870924]],[logseq____&quot;^15logseq____&quot;,[291,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[291,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[291,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[291,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-aae1-442b-80a9-106d75c7e4c4logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Flogseq____&quot;,294,536870924]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Vlogseq____&quot;,294,536870924]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Ulogseq____&quot;,261,536870924]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Ulogseq____&quot;,264,536870924]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Ulogseq____&quot;,281,536870924]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Hlogseq____&quot;,264,536870924]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Hlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Hlogseq____&quot;,281,536870924]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-2ba5-40e6-9147-1a63856c4501logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Schachtelung von quantoren ([Beispiel]([[Beispiele]])):logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Flogseq____&quot;,294,536870924]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Vlogseq____&quot;,307,536870924]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Ulogseq____&quot;,67,536870924]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Ulogseq____&quot;,261,536870924]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Hlogseq____&quot;,67,536870924]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-1f19-4f4a-981d-b52a2605acdflogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[294,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Flogseq____&quot;,307,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Vlogseq____&quot;,307,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Ulogseq____&quot;,261,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-678e-414d-8e6e-bb2be09e72c4logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[295,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Flogseq____&quot;,286,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Vlogseq____&quot;,286,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Ulogseq____&quot;,269,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Ulogseq____&quot;,273,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-9618-4bf6-9b64-b3480b1b4dbalogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[296,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Flogseq____&quot;,297,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Vlogseq____&quot;,313,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Ulogseq____&quot;,221,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Ulogseq____&quot;,225,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Ulogseq____&quot;,282,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Ulogseq____&quot;,285,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Hlogseq____&quot;,221,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Hlogseq____&quot;,225,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Hlogseq____&quot;,282,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Hlogseq____&quot;,285,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-518d-46f1-967a-ec30135d6403logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Aussageform]] (AF) über [Universen]([[Universen (Logik)]]) $U_1,\\\\cdots,U_n$:logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Flogseq____&quot;,313,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Vlogseq____&quot;,313,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Ulogseq____&quot;,283,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Hlogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Hlogseq____&quot;,283,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-ede0-416d-abd5-03690c4653bflogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[298,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Flogseq____&quot;,306,536870924]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Vlogseq____&quot;,313,536870924]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-ac27-4527-bd54-9f8089d7011flogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche Regeln]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Flogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Vlogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Ulogseq____&quot;,262,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Ulogseq____&quot;,267,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Ulogseq____&quot;,270,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Ulogseq____&quot;,271,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Ulogseq____&quot;,277,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Ulogseq____&quot;,278,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Hlogseq____&quot;,262,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Hlogseq____&quot;,267,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Hlogseq____&quot;,270,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Hlogseq____&quot;,271,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Hlogseq____&quot;,277,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Hlogseq____&quot;,278,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-adf2-4676-b39e-de7b7e664562logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Die beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der [[Aussagenlogik]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Flogseq____&quot;,291,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Vlogseq____&quot;,313,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,265,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,284,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Hlogseq____&quot;,265,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Hlogseq____&quot;,284,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-4ddc-4b20-84b4-ee410870b0f1logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;wobei $\\\\pi$ eine \\logseq____&quot;[[Permutation]]\\logseq____&quot; der Zahl $(1,2,\\\\cdots,n)$ istlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Flogseq____&quot;,295,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Vlogseq____&quot;,295,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Ulogseq____&quot;,269,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Ulogseq____&quot;,273,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Ulogseq____&quot;,275,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Hlogseq____&quot;,275,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-5b84-4fec-ae55-40f80b2060b5logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x,y)$ AF in Variablen $x,y$ über $U_1,U_2$\\n\\\\begin{align}\\n\\\\underbrace{\\\\forall x: \\\\underbrace{\\\\exists y: p(x,y)}_{\\\\text{AF in den Variablen }x\\\\text{ über }U_1}}_{\\\\text{Aussage}}\\n\\\\end{align}logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Flogseq____&quot;,293,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Vlogseq____&quot;,293,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,67,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,261,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-fc4b-4e25-9b91-6b16ae812ff4logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist wahr}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Flogseq____&quot;,321,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Vlogseq____&quot;,321,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&quot;,67,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&quot;,269,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&quot;,272,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&quot;,273,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Hlogseq____&quot;,272,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-001a-48f8-aaa8-bd4bc426ca62logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Allquantor]] [[Existenzquantor]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Flogseq____&quot;,290,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Vlogseq____&quot;,290,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,274,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,280,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Hlogseq____&quot;,274,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Hlogseq____&quot;,280,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-c544-4189-a78b-d56c37704e6elogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Widerspruch = ↯, #logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Flogseq____&quot;,320,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Vlogseq____&quot;,320,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,67,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,269,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,272,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,273,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-619b-4863-8922-426cf62535b6logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[306,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Flogseq____&quot;,290,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Vlogseq____&quot;,313,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,217,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Hlogseq____&quot;,217,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-1229-448a-a857-986a1da8c3e8logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Regeln]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Flogseq____&quot;,298,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Vlogseq____&quot;,313,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,261,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,2],536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Hlogseq____&quot;,261,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-ab56-4d55-a726-1f8f4fc82a28logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[308,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Flogseq____&quot;,303,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Vlogseq____&quot;,303,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,67,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,269,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,272,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,273,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-5693-4401-9b83-7ed09f86b127logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[309,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Flogseq____&quot;,312,536870924]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Vlogseq____&quot;,312,536870924]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,67,536870924]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-d182-4cd9-aa08-49df700d5b5dlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXMElogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Flogseq____&quot;,298,536870924]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Vlogseq____&quot;,298,536870924]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ulogseq____&quot;,74,536870924]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Hlogseq____&quot;,74,536870924]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-9133-4ae8-a06d-bd41671fed36logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[311,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Flogseq____&quot;,288,536870924]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Vlogseq____&quot;,288,536870924]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-8b15-4063-a91e-58eeffe68b8dlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Flogseq____&quot;,286,536870924]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Xlogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Vlogseq____&quot;,313,536870924]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,67,536870924]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Hlogseq____&quot;,67,536870924]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u653001de-3474-4873-9d8e-2580b138e681logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 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= Beweisende, auch [q.e.d.]([[Q.E.D.]]), [[w.z.b.w.]], QED, 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[[Potenzen]] und [[Wurzeln]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Flogseq____&quot;,122,536870920]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Vlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,59,536870920]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,69,536870920]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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Dreieck]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Flogseq____&quot;,102,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Vlogseq____&quot;,122,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,60,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,66,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,2],536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Jlogseq____&quot;,[],536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Hlogseq____&quot;,60,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c64f-b083-4d9a-8a6a-091532052952logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\underbrace{\\\\frac6{2+\\\\sqrt2}*\\\\frac{2-\\\\sqrt2}{2-\\\\sqrt2}\\n= \\\\frac{6(2-\\\\sqrt2)}{2^2-(\\\\sqrt2)^2}}_\\\\text{3. binomische Formel}\\nlogseq____&amp;=\\\\frac{6(2-\\\\sqrt2)}2=3(2-\\\\sqrt2)\\\\\\\\\\n\\\\frac{a-b}{\\\\sqrt a+\\\\sqrt b}logseq____&amp;=\\\\frac{a-b}{\\\\sqrt a + \\\\sqrt b}\\\\frac{\\\\sqrt a-\\\\sqrt b}{\\\\sqrt a-\\\\sqrt b}logseq____&amp;, a,b,logseq____&gt;0\\\\notag\\\\\\\\\\n=\\\\frac{(a-b)(\\\\sqrt a-\\\\sqrt b)}{(a-b)}logseq____&amp;=\\\\sqrt a\\\\sqrt b\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Flogseq____&quot;,97,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Vlogseq____&quot;,97,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,59,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,67,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,69,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,71,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,77,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c64f-195d-4825-b47a-3d1ff0af2d07logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Flogseq____&quot;,101,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Vlogseq____&quot;,101,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,60,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,64,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,66,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,70,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Hlogseq____&quot;,70,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c64f-0f46-4150-adb9-604ba70f2bf2logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[91,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 } 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$\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Flogseq____&quot;,82,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Vlogseq____&quot;,82,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,68,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,74,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Hlogseq____&quot;,74,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c64f-683d-4da0-a8a0-c268153e56a4logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Wurzeln]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Flogseq____&quot;,96,536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Vlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,69,536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Jlogseq____&quot;,[],536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Hlogseq____&quot;,69,536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c64f-036f-42a7-9b8c-be366d48d876logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[pq-Formel]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Flogseq____&quot;,85,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Vlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,59,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,61,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,69,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,75,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,2],536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Jlogseq____&quot;,[],536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Hlogseq____&quot;,75,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c64f-089e-4f7a-a539-0c15d43c6216logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[95,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;,536870920]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Flogseq____&quot;,96,536870920]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Vlogseq____&quot;,96,536870920]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,63,536870920]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c64f-f424-4e9c-a7c2-aa467f0e8749logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Logarithmen]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Flogseq____&quot;,117,536870920]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Vlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Ulogseq____&quot;,63,536870920]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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nn=a^1=a\\\\\\\\\\n\\\\sqrt[n]{\\\\frac ab} logseq____&amp;= \\\\frac{\\\\sqrt[n]a}{\\\\sqrt[n]b}\\\\\\\\\\n\\\\left(\\\\sqrt[n]a\\\\right)^mlogseq____&amp;=a^\\\\frac 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[[Binomialkoeffizient]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Flogseq____&quot;,83,536870920]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Xlogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Vlogseq____&quot;,88,536870920]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Ulogseq____&quot;,60,536870920]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Ulogseq____&quot;,64,536870920]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Ulogseq____&quot;,66,536870920]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Ulogseq____&quot;,72,536870920]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____&gt;0$ welche keinen Sinn 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Lösung mit 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von [Punkten]([[Punkte]]) $(x,y)$ in der [Ebene]([[Ebenen]])  die den gleichen [[Abstand]] r ([[Radius]]) zu einem [festen Punkt]([[Fester Punkt]]) 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logseq____&amp;|logseq____&amp;*-1\\\\\\\\\\nxlogseq____&amp;logseq____&gt;-2\\\\\\\\\\nL_1logseq____&amp;=(-2,3)\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Flogseq____&quot;,186,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Xlogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Vlogseq____&quot;,186,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,141,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,154,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,157,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c64f-ed74-4878-9326-25cfef4d7f83logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Kreis]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Flogseq____&quot;,202,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Xlogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Vlogseq____&quot;,212,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,138,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,157,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,2],536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Hlogseq____&quot;,138,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c64f-544f-4efe-9a57-37473a4a21e9logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[170,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;,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Flogseq____&quot;,197,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Xlogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Vlogseq____&quot;,163,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,141,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,154,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,157,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c64f-f836-4e16-9a9d-35fafd49b856logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Der [[Betrag]] ist der zu [[Abstand]] 0\\n\\\\begin{align}\\nf(x)=logseq____&amp;|x|:=logseq____&amp;\\\\begin{cases}\\nxlogseq____&amp;x\\\\ge0\\\\\\\\\\n-xlogseq____&amp;xlogseq____&lt;0\\n\\\\end{cases}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Flogseq____&quot;,202,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Xlogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Vlogseq____&quot;,202,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,157,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Hlogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Hlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c64f-900a-4a23-82a9-eb7edfe46b97logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Flogseq____&quot;,164,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Xlogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Vlogseq____&quot;,161,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,142,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,157,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c64f-ced8-4581-a455-f621bb0e3699logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;wie [[Ellipse]] nur statt [[Summe]] [[Differenz]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Flogseq____&quot;,205,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Xlogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Vlogseq____&quot;,212,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,142,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,153,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,157,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Hlogseq____&quot;,142,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Hlogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Hlogseq____&quot;,153,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c64f-d7da-4e90-ad9f-bcda8970993clogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 1a}\\\\quad x\\\\ge -2$\\n\\\\begin{align}\\n|x+2|logseq____&amp;=x+2\\\\\\\\\\nx-3logseq____&amp;\\\\le x+2 logseq____&amp;|logseq____&amp;+3-x\\\\\\\\\\n0logseq____&amp;\\\\le5\\\\\\\\\\n\\\\end{align}\\n\\\\begin{align}\\nL_1=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|x\\\\ge3,x\\\\ge-2,0\\\\le5\\\\right\\\\}=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|x\\\\ge3\\\\right\\\\}=[3,\\\\infty)\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Flogseq____&quot;,178,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Xlogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Vlogseq____&quot;,163,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,141,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,154,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,157,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c64f-ebd5-4058-a38b-f40acb2d5965logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nK=\\\\left\\\\{(x,y)\\\\in 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(x-x_M)^2+(y-y_M)^2=r^2\\\\right\\\\}\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Flogseq____&quot;,165,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Xlogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Vlogseq____&quot;,169,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,138,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,157,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c64f-bb29-4ee2-b11e-2bdbfdeca69clogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Flogseq____&quot;,198,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Xlogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Vlogseq____&quot;,198,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,141,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,154,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,157,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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1}\\\\quad 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der Gleichung }x^2+\\\\underbrace{4}_p 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Lösung mit 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Multiplikation oder Division mit einem Betrag einer negativen Zahl nicht Anwendbar, da ein [[Betrag]] immer Positiv 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Äquivalentlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^Blogseq____&quot;,1697760848174,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-3e18-49f4-8eb9-fb0194dea3fflogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Klogseq____&quot;,1697760848164,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;tabellenregelnlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^11logseq____&quot;,logseq____&quot;Tabellenregelnlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Blogseq____&quot;,1697760848164,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-9381-4696-b60c-b976ae64522flogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Klogseq____&quot;,1697760848153,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;aussagenlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^11logseq____&quot;,logseq____&quot;Aussagenlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Blogseq____&quot;,1697760848153,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-015e-4516-868f-61648ee39b98logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Klogseq____&quot;,1697760848161,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;verknüpfungenlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^11logseq____&quot;,logseq____&quot;Verknüpfungenlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Blogseq____&quot;,1697760848161,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-6c8d-4e2e-901f-12da7e437fc5logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Klogseq____&quot;,1697760848163,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;aussageformellogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^11logseq____&quot;,logseq____&quot;Aussageformellogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Blogseq____&quot;,1697760848163,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-8bd8-48e4-84c3-fd13ecdae5e5logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Klogseq____&quot;,1697760848157,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;syntaxlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^11logseq____&quot;,logseq____&quot;Syntaxlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Blogseq____&quot;,1697760848157,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-b41d-48a1-be30-923755d5fd84logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Klogseq____&quot;,1697760848153,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;verknüpfung von aussagenlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^11logseq____&quot;,logseq____&quot;Verknüpfung von Aussagenlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Blogseq____&quot;,1697760848153,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-0f71-48a1-ba1a-55d878a76f1elogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Klogseq____&quot;,1697760848173,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;schreibweiselogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^11logseq____&quot;,logseq____&quot;Schreibweiselogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Blogseq____&quot;,1697760848173,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-de44-4712-ba45-64e7f7bd8108logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Klogseq____&quot;,1697760848165,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;belegunglogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^11logseq____&quot;,logseq____&quot;Belegunglogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Blogseq____&quot;,1697760848165,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-2057-47d6-b426-14021d9188bflogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Flogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Vlogseq____&quot;,253,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,67,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Hlogseq____&quot;,67,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-51fa-4fb3-8eb2-d7e9df535fd2logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussagenlogische Variable]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Flogseq____&quot;,242,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Vlogseq____&quot;,253,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Hlogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-cab3-4587-91c7-6f2dc5e5fdd0logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,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;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Flogseq____&quot;,240,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Vlogseq____&quot;,253,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,230,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,236,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Hlogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Hlogseq____&quot;,230,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Hlogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Hlogseq____&quot;,236,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-d8c5-4996-95f0-49dd2f1fc327logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $f$ istlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Flogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Vlogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-fd01-49b8-92dd-b5c25db6b458logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Zuordnung von $w/f$ an jede [Variable]([[Variablen]]) einer [[Aussageformel]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Flogseq____&quot;,248,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Vlogseq____&quot;,248,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,239,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Hlogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Hlogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-0f1d-4ca5-a386-d17ffe729541logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Flogseq____&quot;,258,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Vlogseq____&quot;,253,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Hlogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-b874-420f-88c7-2a95500e0d7flogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wikipedia]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Flogseq____&quot;,267,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Vlogseq____&quot;,247,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Hlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-ad40-4fa1-9245-d39827f9b184logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Büchertiplogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Flogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^17logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-0284-490e-a486-bd567f8d43b4logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Belegung]] (der [[Variablen]])logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Flogseq____&quot;,254,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Vlogseq____&quot;,253,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,239,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Hlogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Hlogseq____&quot;,239,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-19d2-425b-93bd-56b4469289e0logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[249,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;,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Flogseq____&quot;,240,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Vlogseq____&quot;,240,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,67,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-44a7-47a9-8ab6-caad6796ce10logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Flogseq____&quot;,252,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Vlogseq____&quot;,252,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,239,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Hlogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Hlogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Hlogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Hlogseq____&quot;,239,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-122a-4151-a3b4-fafcf9e83968logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $w$ istlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Flogseq____&quot;,264,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Vlogseq____&quot;,264,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-8c45-4fe7-95ba-080993ffac4clogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Flogseq____&quot;,248,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Vlogseq____&quot;,253,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Hlogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Hlogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-2a49-4c8b-a31c-4ef6bc32e3eflogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Verknüpfung von Aussagen]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Flogseq____&quot;,259,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Vlogseq____&quot;,260,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,2],536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Hlogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-c799-4d10-ac61-2cbb9675a928logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussageformel]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Flogseq____&quot;,241,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Vlogseq____&quot;,253,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Hlogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-6a3d-401b-bb2c-f6796208564clogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Flogseq____&quot;,254,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Vlogseq____&quot;,254,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,74,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Hlogseq____&quot;,74,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Hlogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-7968-4244-a3d3-c0fcc5050e22logseq____&quot;,536870923]],[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;,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Flogseq____&quot;,250,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Vlogseq____&quot;,252,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Hlogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-ef93-4319-a9de-f2f816271cd6logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Kontradiktion]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Flogseq____&quot;,264,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Vlogseq____&quot;,253,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Hlogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-17ce-49f1-a245-2d03e3c17e54logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[258,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;,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Flogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Vlogseq____&quot;,253,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,231,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,238,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Hlogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Hlogseq____&quot;,231,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Hlogseq____&quot;,238,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-41bc-427f-8f91-8b66bf48647dlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\nlogseq____&amp;\\logseq____&quot;5\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;\\\\quadlogseq____&amp; (w)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;4\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;logseq____&amp; (f)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Jede gerade Zahl }\\\\ge4\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ ist Summe zweier Primzahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage, }w\\\\text{ oder }f)\\\\notag\\\\\\\\\\nlogseq____&amp;(\\\\text{Vermutung von Goldback 1742})\\\\text{, }logseq____&amp;logseq____&amp;\\\\text{richtig für gerade Zahlen bis }4*10^{18}\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Dieser Satz ist falsch}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{keine Aussage})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Gleichung } x^2+y^2=z^2 \\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ hat eine Lösung }x,y,z\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nlogseq____&amp;x^n+y^n=z^n\\\\text{ eine Lösung}logseq____&amp;logseq____&amp; (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nlogseq____&amp;x,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp;\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Gott ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Nietzsche ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Flogseq____&quot;,262,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Vlogseq____&quot;,260,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-de13-4ba3-90af-ba1570e735fclogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 1. [[Aussagen]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Flogseq____&quot;,247,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Hlogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-ff86-4159-b15e-f3a4049dcaf1logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Variable]([[Variablen]]), die den Wert $w$ oder $f$ annimmtlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Flogseq____&quot;,241,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Vlogseq____&quot;,241,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Hlogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-e93a-435f-b1d8-d26d671c2362logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[262,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;,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Flogseq____&quot;,260,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Vlogseq____&quot;,260,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Hlogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-a214-43f5-ad4d-0b0f03d812e4logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[263,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;,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Flogseq____&quot;,253,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Vlogseq____&quot;,253,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Hlogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-523a-4ee1-9c71-855b961eef67logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Tantologie]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Flogseq____&quot;,252,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Vlogseq____&quot;,253,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Hlogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-8ede-41e8-b8ea-00a5f18caa65logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Weitere [[Beispiele]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Flogseq____&quot;,245,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Vlogseq____&quot;,253,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,67,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Hlogseq____&quot;,67,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-a542-41d4-9d8b-e542133715fdlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[266,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;,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Flogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Xlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,67,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-d734-42b4-b0ef-910abb1a72fblogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;C. Meinel, M. Mundhenk,  [[\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. Auflage 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(logik)logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^11logseq____&quot;,logseq____&quot;Objekt (Logik)logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Blogseq____&quot;,1697760848382,536870924]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-ec94-4a05-b2a8-8aee30503051logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Regeln]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Flogseq____&quot;,299,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Vlogseq____&quot;,322,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Ulogseq____&quot;,269,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Ulogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,2],536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Hlogseq____&quot;,269,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-87b6-4227-a398-44f5e6eeec45logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[295,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Flogseq____&quot;,296,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Vlogseq____&quot;,322,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Ulogseq____&quot;,225,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Ulogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Hlogseq____&quot;,225,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-4c58-4f6b-bb55-907ac1fb15ablogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[296,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Flogseq____&quot;,312,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Vlogseq____&quot;,322,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Ulogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-6494-4ecb-9afe-05b733e5c07flogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Betrachte $\\logseq____&quot;xlogseq____&lt;y\\logseq____&quot;$ als AF über $\\\\Reals, \\\\Reals$logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Flogseq____&quot;,305,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Vlogseq____&quot;,305,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Ulogseq____&quot;,67,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Ulogseq____&quot;,277,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Ulogseq____&quot;,281,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Ulogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-572c-4589-b1a4-464d0857fa68logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[298,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Flogseq____&quot;,303,536870924]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Vlogseq____&quot;,303,536870924]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Ulogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-6a80-4976-ba12-161c428d56d0logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[299,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Flogseq____&quot;,295,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Vlogseq____&quot;,322,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Ulogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-5d9d-4965-b612-d5a858129ef2logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist falsch}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Flogseq____&quot;,318,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Vlogseq____&quot;,297,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,67,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,277,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,280,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,281,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Hlogseq____&quot;,280,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-4f0d-4c2e-8e10-fffa6782738clogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x)$ AF in der Variablen $x$ über $U$:logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Flogseq____&quot;,303,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Vlogseq____&quot;,322,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Ulogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-43dd-44a1-aa5b-057ed0b68b7blogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[302,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Flogseq____&quot;,318,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Vlogseq____&quot;,318,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,67,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,277,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,280,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,281,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-b5e2-4ada-8e08-a08996369f04logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[303,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Flogseq____&quot;,324,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Vlogseq____&quot;,322,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-94f2-4397-a654-46a0db09bdc3logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Flogseq____&quot;,310,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Vlogseq____&quot;,310,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,269,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,272,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,284,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,289,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Hlogseq____&quot;,272,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Hlogseq____&quot;,284,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Hlogseq____&quot;,289,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-fb7a-45fb-b6be-a60a0e49d726logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Flogseq____&quot;,326,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Vlogseq____&quot;,315,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,67,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,277,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,281,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Hlogseq____&quot;,67,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-8465-4852-b353-99976160fdcclogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche Regeln]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Flogseq____&quot;,328,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Vlogseq____&quot;,328,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,270,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,275,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,278,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,285,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,286,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Hlogseq____&quot;,270,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Hlogseq____&quot;,275,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Hlogseq____&quot;,278,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Hlogseq____&quot;,279,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Hlogseq____&quot;,285,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Hlogseq____&quot;,286,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-8c6a-4eeb-9b84-ecdee4e34b43logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Flogseq____&quot;,315,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Vlogseq____&quot;,322,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,67,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Hlogseq____&quot;,67,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-9128-4853-acd0-48542a793b1clogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Verschiedene [[Quantoren]] dürfen **nicht** vertauscht werdenlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Flogseq____&quot;,321,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Vlogseq____&quot;,326,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,277,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,281,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Hlogseq____&quot;,281,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-f1af-4e78-8723-b36a44ab1b3dlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[309,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: 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Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Flogseq____&quot;,309,536870924]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Vlogseq____&quot;,322,536870924]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-644a-4515-9ac9-df53013c0942logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Regeln]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Flogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Vlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,269,536870924]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Quantoren]] dürfen vertauscht 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von quantoren 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x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist 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= Beweisende, auch [q.e.d.]([[Q.E.D.]]), [[w.z.b.w.]], QED, 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(AF) über [Universen]([[Universen (Logik)]]) 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$\\\\pi$ eine \\logseq____&quot;[[Permutation]]\\logseq____&quot; der Zahl $(1,2,\\\\cdots,n)$ 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[[Aussagenlogik]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Flogseq____&quot;,301,536870924]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Vlogseq____&quot;,322,536870924]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ulogseq____&quot;,273,536870924]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ulogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ulogseq____&quot;,292,536870924]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Hlogseq____&quot;,273,536870924]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Hlogseq____&quot;,292,536870924]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-f87f-40cc-b98f-48bfaf535240logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Flogseq____&quot;,331,536870924]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Vlogseq____&quot;,322,536870924]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Ulogseq____&quot;,67,536870924]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Ulogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Hlogseq____&quot;,67,536870924]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-da24-45ad-8246-5785a15a1526logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[325,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Flogseq____&quot;,300,536870924]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Vlogseq____&quot;,300,536870924]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ulogseq____&quot;,67,536870924]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ulogseq____&quot;,277,536870924]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ulogseq____&quot;,280,536870924]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ulogseq____&quot;,281,536870924]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ulogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-f3ac-4072-b052-be0313cf6c68logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nlogseq____&amp;\\\\forall 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[[Allquantor]] [[Existenzquantor]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Flogseq____&quot;,296,536870924]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Xlogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Vlogseq____&quot;,296,536870924]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Ulogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Ulogseq____&quot;,282,536870924]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Ulogseq____&quot;,287,536870924]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Ulogseq____&quot;,288,536870924]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Hlogseq____&quot;,282,536870924]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Hlogseq____&quot;,288,536870924]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c650-6d08-471c-a7ba-26fb5e959ffflogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[328,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n(p\\\\land 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