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[[Potenzen]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Flogseq____&quot;,96,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Vlogseq____&quot;,96,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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} x=\\\\frac25 \\\\text{ und } y=\\\\frac37 \\\\text{ ist }\\\\frac xy$\\n\\\\begin{align}\\n\\\\frac xy = \\\\frac{\\\\frac25}{\\\\frac37} = 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x)^5logseq____&amp;=2+20x+40x^2\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Flogseq____&quot;,76,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Vlogseq____&quot;,53,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a89-b54a-4059-8ce2-a373f095e86blogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;![draws/2023-10-08-21-23-31.excalidraw](../assets/excalidraw_svg/2023-10-08-21-23-31.svg)logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Flogseq____&quot;,57,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Vlogseq____&quot;,61,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a89-d745-458a-b0bb-5457a75864cdlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____&gt;0$ welche keinen Sinn ergibtlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Flogseq____&quot;,66,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Vlogseq____&quot;,66,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Hlogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a89-21c6-47f5-9890-4f17c57359dflogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{array}{c} (a+b)^0logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;1 \\\\\\\\\\n(a+b)^1logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;1 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^2logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 2 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^3logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;1 logseq____&amp;logseq____&amp; 3 logseq____&amp;logseq____&amp; 3 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^4logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 4 logseq____&amp;logseq____&amp; 6 logseq____&amp;logseq____&amp; 4 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^5logseq____&amp;logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 5 logseq____&amp;logseq____&amp; 10 logseq____&amp;logseq____&amp; 10 logseq____&amp;logseq____&amp; 5 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^6logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 6 logseq____&amp;logseq____&amp; 15 logseq____&amp;logseq____&amp; 20 logseq____&amp;logseq____&amp; 15 logseq____&amp;logseq____&amp; 6 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^7logseq____&amp;1 logseq____&amp;logseq____&amp; 7 logseq____&amp;logseq____&amp;21 logseq____&amp;logseq____&amp; 35 logseq____&amp;logseq____&amp; 35 logseq____&amp;logseq____&amp; \\\\cdots\\\\end{array}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Flogseq____&quot;,53,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Vlogseq____&quot;,53,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a89-0c4f-4034-9ff3-6ff090651c3clogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Allgemein}$\\n\\\\begin{align}\\n(a+b)^2logseq____&amp;=a^2+2ab+b^2logseq____&amp;,\\\\text{ 1. Binomische Formel}\\\\\\\\\\n(a-b)^2logseq____&amp;=a^2-2ab+b^2logseq____&amp;,\\\\text{ 2. Binomische Formel}\\\\\\\\\\n(a+b)(a-b)logseq____&amp;=a^2-b^2logseq____&amp;,\\\\text{ 3. Binomische Formel}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Flogseq____&quot;,89,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Vlogseq____&quot;,89,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a89-0ff4-417b-a7b0-ab6183c66989logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel für die 3. Binomische Formel}$\\n\\\\begin{align}\\n\\\\frac{\\\\frac1{a-b}+\\\\frac1{a+b}}{\\\\frac1{a-b}-\\\\frac1{a+b}}\\nlogseq____&amp;=\\\\frac{\\\\frac{a+b+a-b}{(a+b)*(a-b)}}{\\\\frac{a+b-(a-b)}{(a+b)*(a-b)}}\\nlogseq____&amp;=\\\\frac{a+b+a-b}{a+b-a+b}\\nlogseq____&amp;=\\\\frac{2a}{2b}\\nlogseq____&amp;=\\\\frac ab\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Flogseq____&quot;,77,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Vlogseq____&quot;,89,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a89-5d0b-48f8-93a8-5ae815c9e320logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Alte Schreibweise}$\\n\\\\begin{align}\\n\\\\text{cosa }logseq____&amp;\\\\text{plus }logseq____&amp;\\\\text{cubus }logseq____&amp;\\\\text{acq }logseq____&amp;6\\\\\\\\\\nxlogseq____&amp;+logseq____&amp;x^3logseq____&amp;=logseq____&amp;6\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Flogseq____&quot;,50,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Vlogseq____&quot;,62,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a89-f07b-45c0-b75b-c444b2058466logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;https://www.wolframalpha.comlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Flogseq____&quot;,63,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Vlogseq____&quot;,63,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ulogseq____&quot;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ulogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a89-d9ca-40ff-83b1-7e631e2679aalogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Quadratische Gleichungen]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Flogseq____&quot;,54,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Vlogseq____&quot;,96,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Hlogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a89-18bb-42fb-ac55-c981a43057celogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[82,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 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logseq____&amp; a,blogseq____&gt;0\\\\\\\\\\na^2b^2logseq____&amp;=(ab)^n\\\\\\\\\\n\\\\frac{a^n}{b^n}logseq____&amp;=\\\\left(\\\\frac 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$(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Flogseq____&quot;,73,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Vlogseq____&quot;,73,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Hlogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a89-6f68-409b-ad9f-85cf43b8c333logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn }alogseq____&gt;0\\\\text{, 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ba x + \\\\frac ca logseq____&amp;= 0\\\\\\\\\\nplogseq____&amp;=\\\\frac ba,logseq____&amp;q = \\\\frac 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[[Wurzelgleichung]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Flogseq____&quot;,81,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Vlogseq____&quot;,96,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,30,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Trigonometrie]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Flogseq____&quot;,55,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Vlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Binomialkoeffizient]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Flogseq____&quot;,73,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Vlogseq____&quot;,53,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,32,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Hlogseq____&quot;,32,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a89-93e6-43ef-bf41-7540b316c4fblogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten 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1. [[Aussagen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Flogseq____&quot;,183,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Xlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Vlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Hlogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-49c0-4c51-a5d9-4d0e44211d27logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Flogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Xlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Vlogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Hlogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-3e27-4f58-aef2-6b8c736b546dlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\np\\\\land q\\\\lor r\\\\\\\\\\n(p\\\\land q)\\\\lor r\\\\\\\\\\np\\\\land (q\\\\lor r)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Flogseq____&quot;,185,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Xlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Vlogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-dfca-4741-aa84-8f5967065addlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $w$ istlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Flogseq____&quot;,188,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Xlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Vlogseq____&quot;,188,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-8429-47e5-93cf-7559b63f0062logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Flogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Xlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Vlogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Hlogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Hlogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-1c23-4e65-8426-6c0529f9a4e4logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formeln $p,q$ [[logisch äquivalent]], wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Flogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Xlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Vlogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,144,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,161,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Hlogseq____&quot;,144,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Hlogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Hlogseq____&quot;,161,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-3e57-4689-9dbd-bfec45f38195logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Soweit die \\logseq____&quot;[[Syntax]]\\logseq____&quot;, jetzt die [[Semantik]]. Die [[Wahrheitswert]]e\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Flogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Xlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Vlogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Hlogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Hlogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Hlogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Hlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-189e-4967-bb17-dcbd4a8e6517logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Flogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Xlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Vlogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,144,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Hlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Hlogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Hlogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Hlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-2bac-4245-a068-5a8a5fdf2adflogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $f$ istlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Flogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Xlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Vlogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,151,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-3ae7-4fc2-a137-3568697275f9logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Verknüpfung von Aussagen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Flogseq____&quot;,181,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Xlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Vlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Hlogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-c694-4fc1-a24a-f1af5234776alogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;C. Meinel, M. Mundhenk, [[\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. Auflage 2011]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Flogseq____&quot;,183,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Xlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Vlogseq____&quot;,183,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,149,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Hlogseq____&quot;,149,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-60e6-4114-9ca9-61ba47de1ce3logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Flogseq____&quot;,163,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Xlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Vlogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,144,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Hlogseq____&quot;,144,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Hlogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-2b13-477d-8107-02a3617c7d84logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Weitere Beispiel}$\\n\\\\begin{align}\\n(p\\\\rightarrow q)logseq____&amp;\\\\equiv((\\\\neg q)\\\\rightarrow(\\\\neg p))\\\\\\\\\\n(p\\\\land(p\\\\rightarrow q)) logseq____&amp;\\\\rightarrow q logseq____&amp;\\\\quad 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[[Kontradiktion]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Flogseq____&quot;,188,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Xlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Vlogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,151,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Hlogseq____&quot;,151,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-ed6b-4578-944b-f933ef45588dlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Zuordnung von $w/f$ an jede [[Variable]] einer [[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Flogseq____&quot;,163,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Xlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Vlogseq____&quot;,163,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Hlogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Hlogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-dee3-4fa8-aa17-b421d8a28324logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Satz, der wahr oder falsch ist, d.h. der [[Wahrheitswert]] $w$ bzw $f$ hat ($t/f$, $1/0$, $\\\\text{wahr}/\\\\text{falsch}$)logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Flogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Xlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Vlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Hlogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-0c55-4e9b-8ac5-a9caeaee1f34logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\nlogseq____&amp;\\logseq____&quot;5\\\\text{ 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}x,y,z\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nlogseq____&amp;x^n+y^n=z^n\\\\text{ eine Lösung}logseq____&amp;logseq____&amp; (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nlogseq____&amp;x,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp;\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Gott ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Nietzsche ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Flogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Xlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Vlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-5f1b-45ae-9e25-476514c1a637logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wikipedia]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Flogseq____&quot;,175,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Xlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Vlogseq____&quot;,183,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,146,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Hlogseq____&quot;,146,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-cb47-43c8-ab8a-7b749f96fc16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 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logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^17logseq____&quot;,false,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-1081-44c3-bfc0-a54eade50eeflogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Flogseq____&quot;,187,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Xlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Vlogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Hlogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-04ba-43ab-ac4e-5a52629e3ff2logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sind $p$ und $q$ [[Aussagen]], so auch\\n\\\\begin{align}\\n(p\\\\land q) logseq____&amp;\\\\quadlogseq____&amp; (\\logseq____&quot;\\\\text{und}\\logseq____&quot;)\\\\\\\\\\n(p\\\\lor q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{oder}\\logseq____&quot;)\\\\\\\\\\n(\\\\neg p) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{nicht}\\logseq____&quot;)\\\\\\\\\\n(p\\\\rightarrow q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{impliziert}\\logseq____&quot;)\\\\\\\\\\n(p\\\\leftrightarrow q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{genau dann 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Bestimmung des }$[[Wahrheitswerteverlauf]]$\\\\text{ von }(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)$\\n|$p$|$q$||$p\\\\rightarrow q$|$q\\\\rightarrow p$|$(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)|$p\\\\leftrightarrow q$|\\n|-|-|-|-|-|-|\\n|f|f||w|w|w|w|\\n|f|w||w|f|f|f|\\n|w|f||f|w|f|f|\\n|w|w||w|w|w|w|logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Flogseq____&quot;,172,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Xlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Vlogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,144,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Hlogseq____&quot;,144,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65286a8a-8bc5-492c-bdc0-e6242d0d1d0flogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### 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