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Wissensabgleich [[Logarithmen]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Flogseq____&quot;,103,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,31,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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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;,57,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Vlogseq____&quot;,57,536870919]],[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;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978d9-b3c1-40c1-8bb4-32dfc3e5fc5flogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]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;,69,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Vlogseq____&quot;,55,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Hlogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978d9-5785-4a0e-9dd8-e298dbbb64a5logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Pascalsches Dreieck]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Flogseq____&quot;,83,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Vlogseq____&quot;,95,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Hlogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978d9-bbbc-46e6-b365-da6e03ecb2e9logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn }alogseq____&gt;0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=a\\\\sqrt{a}logseq____&amp;,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=a^2-\\\\sqrt{a}logseq____&amp;,f\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=\\\\sqrt{a^3}logseq____&amp;,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=a^{\\\\frac32}logseq____&amp;,r\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Flogseq____&quot;,96,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Vlogseq____&quot;,96,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978d9-d96a-48b8-9b49-2034689fa87flogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Potenzen]] und [[Wurzeln]]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;,95,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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0}\\n\\\\\\\\\\n{1\\\\choose 0} {1\\\\choose 1}\\n\\\\\\\\\\n{2\\\\choose 0} {2\\\\choose 1} {2\\\\choose 2}\\n\\\\\\\\\\n{3\\\\choose 0} {3\\\\choose 1} {3\\\\choose 2} {3\\\\choose 3}\\n\\\\\\\\\\n\\\\cdots\\n\\\\end{array}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;,56,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Vlogseq____&quot;,47,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,32,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978d9-1d9e-42c5-b283-f28ce7c2e001logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche }$[[Gleichungen]]$\\\\text{ sind richtig?}$\\n\\\\begin{align}\\ne^{x+y} logseq____&amp;= e^x + e^y logseq____&amp; ,f \\\\\\\\\\ne^{x+y} logseq____&amp;= e^x * x^y logseq____&amp; ,r \\\\\\\\\\ne^{x+y}logseq____&amp;=e^{xy} logseq____&amp; ,f\\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=x+y logseq____&amp; ,x+ylogseq____&gt;c \\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=e^x*e^ylogseq____&amp;,f\\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=ln(e^x+y)logseq____&amp;,x+ylogseq____&gt;0\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Flogseq____&quot;,103,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Vlogseq____&quot;,103,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ulogseq____&quot;,33,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Hlogseq____&quot;,33,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978d9-a08f-430f-a076-9d83c76f5d8elogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Allgemein}$\\n\\\\begin{align}\\n\\\\ln a + \\\\ln b logseq____&amp;= \\\\ln(a*b) \\\\\\\\\\n\\\\ln(-a) logseq____&amp;= \\\\frac1{\\\\ln 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(50) hat angeblich noch ne Zeile $=x^0+3ylogseq____&gt;0$ welche keinen Sinn 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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;,[83,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Flogseq____&quot;,58,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Vlogseq____&quot;,95,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978d9-9e2c-4f2c-ab12-5670b2066646logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])logseq____&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;,65,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Vlogseq____&quot;,65,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Hlogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978d9-af09-4c87-b704-e11f65745581logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Flogseq____&quot;,63,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Vlogseq____&quot;,86,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Hlogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978d9-ac9e-419a-9442-daed89507bfflogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Rationalmachen]] des [[Nenner]]slogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Flogseq____&quot;,87,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Vlogseq____&quot;,98,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Hlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Hlogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978d9-8bb9-4d72-8919-3614041f21b0logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Allgemein}$\\n\\\\begin{align}\\n|y|logseq____&amp;=\\\\begin{cases}\\ny logseq____&amp;\\\\text{ falls } y\\\\ge0\\\\\\\\\\n-y logseq____&amp;\\\\text{ falls } ylogseq____&lt;0\\\\\\\\\\n\\\\end{cases}\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Flogseq____&quot;,68,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Vlogseq____&quot;,98,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978d9-d038-4825-a4ac-1a0c2c2a327flogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Wurzelgleichung]]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;,54,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Vlogseq____&quot;,77,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,30,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Hlogseq____&quot;,30,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978d9-5a14-4875-bc44-81d3c31c1acalogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Für } x=\\\\frac25 \\\\text{ und } y=\\\\frac37 \\\\text{ ist }\\\\frac xy$\\n\\\\begin{align}\\n\\\\frac xy = \\\\frac{\\\\frac25}{\\\\frac37} = \\\\frac{2*7}{3*5}=\\\\frac{14}{15}\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Flogseq____&quot;,66,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Vlogseq____&quot;,66,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978d9-8c9d-442c-a6c9-e58e0673f6c1logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\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;,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Flogseq____&quot;,60,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Vlogseq____&quot;,60,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,26,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Hlogseq____&quot;,26,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978d9-505a-4edf-9d98-f5348de0c2dalogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[91,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;,[91,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Flogseq____&quot;,80,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Vlogseq____&quot;,103,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978d9-0c0c-4270-ba7e-69aa427b8637logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[92,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;,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Flogseq____&quot;,85,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Vlogseq____&quot;,85,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978d9-572f-4952-adfe-8379e218b02elogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])\\n\\\\begin{align}\\nx^4-34x^2+225logseq____&amp;=0\\\\\\\\\\n\\\\text{substituiert }ylogseq____&amp;=x^2\\\\\\\\\\ny^2-34y+225logseq____&amp;=0\\\\\\\\\\ny_{1,2}logseq____&amp;=17\\\\pm\\\\sqrt{(-17)^2-225}\\\\\\\\\\nlogseq____&amp;=17\\\\pm\\\\sqrt{289-225}\\nlogseq____&amp;=17\\\\pm\\\\sqrt{64}=17\\\\pm8\\\\\\\\\\nlogseq____&amp;=\\\\left.\\\\begin{cases}\\n25\\\\\\\\\\n9\\n\\\\end{cases}\\\\right|\\\\begin{array}{l}\\nx^2=25logseq____&amp;\\\\rightarrow logseq____&amp;x_1=5;logseq____&amp;x_2=-5\\\\\\\\\\nx^2=9logseq____&amp;\\\\rightarrow logseq____&amp;x_1=3;logseq____&amp;x_2=-3\\\\\\\\\\n\\\\end{array}\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Flogseq____&quot;,65,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Vlogseq____&quot;,60,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Hlogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978d9-8a3d-4644-a7a0-8f8f9c55be19logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn } 10^x=y \\\\text{, dann}$\\n\\\\begin{align}\\nxlogseq____&amp;=\\\\lg y logseq____&amp; ,r\\\\\\\\\\nxlogseq____&amp;=\\\\log_y10logseq____&amp;,f\\\\\\\\\\nxlogseq____&amp;=\\\\log_{10}ylogseq____&amp;,r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&amp;= \\\\ln 2 logseq____&amp;, r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&amp;= \\\\ln 8 logseq____&amp;, f \\\\\\\\\\n\\\\ln 4 + \\\\ln 2 logseq____&amp;= \\\\ln 8 logseq____&amp;, r \\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Flogseq____&quot;,72,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Vlogseq____&quot;,72,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,31,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978d9-6ac5-49ee-be43-4814d15cbfdclogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Binomische 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2}\\\\quad xlogseq____&lt;3$\\n\\\\begin{align}\\n|\\\\underbrace{x-3}_{logseq____&lt;0}|logseq____&amp;=6(x-3)=-x+3\\\\\\\\\\n-x+3logseq____&amp;\\\\le|x+2|\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Flogseq____&quot;,132,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Vlogseq____&quot;,144,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-6bda-47e4-8602-555b27575ff5logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[136,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 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[[Betrag]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^Flogseq____&quot;,120,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^Vlogseq____&quot;,116,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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$\\\\infty$\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|xlogseq____&gt;4\\\\right\\\\}=:(4,\\\\infty)\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Flogseq____&quot;,133,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Vlogseq____&quot;,120,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-e2ec-4c09-9a28-c7d3b11fb0aalogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\{a,b,c\\\\}$logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Flogseq____&quot;,116,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Vlogseq____&quot;,116,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-766f-43ef-a922-ab3959daf508logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Flogseq____&quot;,137,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Vlogseq____&quot;,137,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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logseq____&amp;|logseq____&amp;+3\\\\\\\\\\nxlogseq____&amp;logseq____&lt;8\\\\\\\\\\nL_2logseq____&amp;=[3,8)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Flogseq____&quot;,134,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Vlogseq____&quot;,130,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-f59b-4724-afb2-ba5e832b1164logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Kombinieren:\\n\\\\begin{align}\\nL=L_1\\\\cup L_2=[3,\\\\infty)\\\\cup\\\\left[\\\\frac12,3\\\\right)=\\\\left[\\\\frac12,\\\\infty\\\\right)\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Flogseq____&quot;,155,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Vlogseq____&quot;,144,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-c8b9-44e3-a6d3-251520c905eelogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Flogseq____&quot;,150,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Vlogseq____&quot;,150,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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Aussagenlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Blogseq____&quot;,1697216730305,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-8657-4982-a04b-a90d5534d0b0logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Klogseq____&quot;,1697216730318,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^@logseq____&quot;,false,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;schreibweiselogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^11logseq____&quot;,logseq____&quot;Schreibweiselogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Blogseq____&quot;,1697216730318,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-2ff1-4a31-a1af-1d0c6028d25alogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Klogseq____&quot;,1697216730315,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^@logseq____&quot;,false,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;belegunglogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^11logseq____&quot;,logseq____&quot;Belegunglogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Blogseq____&quot;,1697216730315,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-37a9-4d43-941b-f19a6051e9e1logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $f$ istlogseq____&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;,207,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Vlogseq____&quot;,207,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,169,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-8051-4036-8b41-ab34f0bc5335logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Zuordnung von $w/f$ an jede [Variable]([[Variablen]]) einer [[Aussageformel]]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;,183,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Vlogseq____&quot;,183,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Hlogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Hlogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-7523-447a-866d-c6aeb7c65435logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Belegung]] (der [[Variablen]])logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Flogseq____&quot;,208,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Vlogseq____&quot;,188,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ulogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Hlogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Hlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-9089-47e6-991c-daa645863734logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]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;,189,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Vlogseq____&quot;,188,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Hlogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-f399-4d51-981a-f1d9e3fd711flogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Flogseq____&quot;,200,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Vlogseq____&quot;,188,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Hlogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-2cb2-4d30-971a-3c0f46792f49logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[186,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;,[186,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Flogseq____&quot;,198,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Vlogseq____&quot;,198,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Hlogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-2d66-4768-9c27-3b0df940aaaelogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel: Bestimmung des }$[[Wahrheitswerteverlauf]]$\\\\text{ von }(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)$\\n|$p$|$q$||$p\\\\rightarrow q$|$q\\\\rightarrow p$|$(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)|$p\\\\leftrightarrow q$|\\n|-|-|-|-|-|-|\\n|f|f||w|w|w|w|\\n|f|w||w|f|f|f|\\n|w|f||f|w|f|f|\\n|w|w||w|w|w|w|logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Flogseq____&quot;,206,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Vlogseq____&quot;,197,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Hlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-e27c-4c4e-9b5a-b80e17f2ff8alogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Verknüpfung von Aussagen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Flogseq____&quot;,191,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Vlogseq____&quot;,198,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Hlogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-b8fa-4f1b-bfbf-4355a7b1a6eelogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sind $p$ und $q$ [[Aussagen]], so auch\\n\\\\begin{align}\\n(p\\\\land q) logseq____&amp;\\\\quadlogseq____&amp; (\\logseq____&quot;\\\\text{und}\\logseq____&quot;)\\\\\\\\\\n(p\\\\lor q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{oder}\\logseq____&quot;)\\\\\\\\\\n(\\\\neg p) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{nicht}\\logseq____&quot;)\\\\\\\\\\n(p\\\\rightarrow q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{impliziert}\\logseq____&quot;)\\\\\\\\\\n(p\\\\leftrightarrow q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{genau dann wenn}\\logseq____&quot;)\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Flogseq____&quot;,188,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Vlogseq____&quot;,188,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Hlogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-10f5-4eb0-bc43-61573e519566logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Tantologie]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Flogseq____&quot;,197,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Vlogseq____&quot;,188,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Hlogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-8c22-4205-a0a2-00d77513a432logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\nlogseq____&amp;\\logseq____&quot;5\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;\\\\quadlogseq____&amp; (w)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;4\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;logseq____&amp; (f)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Jede gerade Zahl }\\\\ge4\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ ist Summe zweier Primzahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage, }w\\\\text{ oder }f)\\\\notag\\\\\\\\\\nlogseq____&amp;(\\\\text{Vermutung von Goldback 1742})\\\\text{, }logseq____&amp;logseq____&amp;\\\\text{richtig für gerade Zahlen bis }4*10^{18}\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Dieser Satz ist falsch}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{keine Aussage})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Gleichung } x^2+y^2=z^2 \\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ hat eine Lösung }x,y,z\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nlogseq____&amp;x^n+y^n=z^n\\\\text{ eine Lösung}logseq____&amp;logseq____&amp; (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nlogseq____&amp;x,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp;\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Gott ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Nietzsche ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Flogseq____&quot;,186,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Vlogseq____&quot;,198,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-ca44-4cae-8206-b7af2d645011logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $w$ istlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Flogseq____&quot;,190,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Vlogseq____&quot;,190,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-2761-467e-9bba-d96fac88510clogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Büchertiplogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Flogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Vlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^17logseq____&quot;,false,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-ad57-49bd-992d-e2c266efd76alogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Variable]([[Variablen]]), die den Wert $w$ oder $f$ annimmtlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Flogseq____&quot;,201,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Vlogseq____&quot;,201,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,163,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Hlogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-7c7b-48fc-837d-847dba68bd89logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Soweit die \\logseq____&quot;[[Syntax]]\\logseq____&quot;, jetzt die [[Semantik]]. Die [Wahrheitswerte]([[Wahrheitswert]])\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Flogseq____&quot;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Vlogseq____&quot;,188,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,171,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,177,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Hlogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Hlogseq____&quot;,171,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Hlogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Hlogseq____&quot;,177,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-c6c0-4de5-ba76-067f200176e9logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[196,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;,[196,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Flogseq____&quot;,193,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Vlogseq____&quot;,193,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Hlogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-24ee-4142-a8cb-05067d3ac608logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Flogseq____&quot;,183,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Vlogseq____&quot;,188,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Hlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Hlogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-4438-4716-b7f9-0760fec70081logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 1. [[Aussagen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Flogseq____&quot;,193,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Vlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Hlogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-8b54-470e-a86d-c01533144650logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[199,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;,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Flogseq____&quot;,202,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Vlogseq____&quot;,202,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-9bd7-408a-89ff-c72fb59c264alogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formeln $p,q$ [[logisch äquivalent]], wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv 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durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt 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mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach 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(Logik)logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Blogseq____&quot;,1697216730517,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-1748-4d9e-9788-05de0e6de4f4logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Klogseq____&quot;,1697216730520,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;[]aussagenlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^11logseq____&quot;,logseq____&quot;[]Aussagenlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Blogseq____&quot;,1697216730520,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-4785-44d8-b245-9d40d0173435logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche Regeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Flogseq____&quot;,247,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Vlogseq____&quot;,247,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,211,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,219,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,226,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Hlogseq____&quot;,211,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Hlogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Hlogseq____&quot;,219,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Hlogseq____&quot;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Hlogseq____&quot;,226,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Hlogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-0f03-488e-a0ea-22c30a074f29logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $x$ aus $\\\\Reals$ beliebig. Setze $y:=x+1$ (ist aus $\\\\Reals$). Dann ist $xlogseq____&lt;x+1=y$ also $xlogseq____&lt;y$. $\\\\blacksquare$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Flogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Vlogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-e5d0-4536-9740-716583a867f5logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativschreibweisen:\\n$\\\\forall x: p(x)$ auch $\\\\bigwedge x:p(x)$\\n$\\\\exists x:p(x)$ auch $\\\\bigvee x:p(x)$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Flogseq____&quot;,246,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Vlogseq____&quot;,244,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-6076-463b-9f0b-72767ed1aca6logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])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;,248,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Vlogseq____&quot;,244,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Hlogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-a39f-4600-9152-475b7132b686logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Widerspruch = ↯, #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;,262,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Vlogseq____&quot;,262,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-8f69-4957-8cee-c3fcd1364db1logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Schachtelung von quantoren ([Beispiel]([[Beispiele]])):logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Flogseq____&quot;,272,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Vlogseq____&quot;,259,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Hlogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-d8e9-4238-b06d-f23d482a497dlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x,y)$ AF in Variablen $x,y$ über $U_1,U_2$\\n\\\\begin{align}\\n\\\\underbrace{\\\\forall x: \\\\underbrace{\\\\exists y: p(x,y)}_{\\\\text{AF in den Variablen }x\\\\text{ über }U_1}}_{\\\\text{Aussage}}\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Flogseq____&quot;,241,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Vlogseq____&quot;,241,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-82c6-439e-aa4b-93b5f3ac3e7blogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\forall x:p(x)$ ist die [Aussage]([[[]Aussagen]]): $\\logseq____&quot;\\\\text{Für alle x aus U ist p(x) wahr}\\logseq____&quot;\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w\\\\quadlogseq____&amp;\\\\text{fallls p(x) w für alle x aus U}\\\\\\\\f\\\\quadlogseq____&amp;\\\\text{falls p(x) f für (wenigstens) ein x aus U}\\\\end{cases}$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Flogseq____&quot;,250,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Vlogseq____&quot;,250,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,166,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Hlogseq____&quot;,166,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Hlogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-58b2-4cb1-ac63-37f857cd070dlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Aussageform]]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;,247,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Vlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Hlogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-9709-44f6-baa9-1fabdb717df2logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist falsch}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Flogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Vlogseq____&quot;,251,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Hlogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-873b-4ad6-8a6e-95bb333c76f4logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\exists x:p(x)$ ist die Aussage: \\logseq____&quot;Es gibt (wenigstens) ein x aus U für das $p(x)$ wahr ist\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w \\\\quadlogseq____&amp;\\\\text{falls }p(x)\\\\text{ w ist für (wenigstens) ein x aus U}\\\\\\\\f\\\\quad logseq____&amp;\\\\text{falls }p(x)\\\\text{ f ist für alle x aus U}\\\\end{cases}$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Flogseq____&quot;,270,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Vlogseq____&quot;,244,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,166,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Hlogseq____&quot;,166,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-763c-4c52-948e-0f961cd0f57flogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n(p\\\\land q)\\\\land r logseq____&amp;\\\\equiv p\\\\land(q\\\\land r),\\\\quadlogseq____&amp;\\\\text{schreibe daher: }  p\\\\land q\\\\land r,\\\\quad \\\\land \\\\text{ assoziativ}\\\\\\\\\\n(p \\\\lor q) \\\\lor r logseq____&amp;\\\\equiv p \\\\lor (q\\\\lor r),\\\\quadlogseq____&amp;\\\\text{schreibe daher: } p\\\\lor q\\\\lor r,\\\\quad \\\\lor \\\\text{ assoziativ}\\\\\\\\\\np \\\\land q logseq____&amp;\\\\equiv q \\\\land p,\\\\quad \\\\land logseq____&amp;\\\\text{ kommutativ}\\\\\\\\\\np \\\\lor q logseq____&amp;\\\\equiv q \\\\lor p,\\\\quad \\\\lor logseq____&amp;\\\\text{ kommutativ}\\\\\\\\\\n\\\\neg(\\\\neg p) logseq____&amp;\\\\equiv p, \\\\quad \\\\neg logseq____&amp;\\\\text{ idenpotent}\\\\\\\\\\np\\\\land(q\\\\lor r)logseq____&amp;\\\\equiv (p\\\\land q)\\\\lor(p\\\\land r);\\\\notag\\\\\\\\\\np\\\\lor(q\\\\land r)logseq____&amp;\\\\equiv (p\\\\lor q)\\\\lor(p\\\\land r),\\\\quad logseq____&amp;\\\\land,\\\\lor\\\\text{ wechselseitig distributiv}\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&amp;\\\\equiv(\\\\neg p)\\\\lor(\\\\neg q);\\\\notag\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&amp;\\\\equiv(\\\\neg p)\\\\land (\\\\neg q), \\\\quad logseq____&amp;\\\\text{ (kleine) de Morgansche Regeln}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Flogseq____&quot;,258,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Vlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-9627-477c-84e2-738c0a84c5c6logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Gleichartige]([[Gleichartig]]) [[Quantoren]] dürfen vertauscht werdenlogseq____&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;,259,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Vlogseq____&quot;,244,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Hlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Hlogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-da1a-47b8-98ee-1021ad210523logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Satz]] mit [[Variablen]] $x_1,\\\\cdots,x_n$, der bei Ersetzung jedes $x_j$ durch ein [Objekt]([[Objekt (Logik)]]) aus $U_j$ stets zu einer [Aussage]([[Aussagen]]) wirdlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Flogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Vlogseq____&quot;,244,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,170,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,174,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,231,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Hlogseq____&quot;,170,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Hlogseq____&quot;,174,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Hlogseq____&quot;,231,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Hlogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-4c7a-495b-a040-6e603d86c95flogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x)$ AF in der Variablen $x$ über $U$: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;,254,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Vlogseq____&quot;,244,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-258c-4981-bf12-bf5dbb131e5clogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Betrachte $\\logseq____&quot;xlogseq____&lt;y\\logseq____&quot;$ als AF über $\\\\Reals, \\\\Reals$logseq____&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;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Vlogseq____&quot;,264,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-e43c-4c24-969c-8d91a85c4f6blogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]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;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Vlogseq____&quot;,244,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Hlogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-dfa4-40ef-86b1-8d00f2e9bcealogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\blacksquare$ = Beweisende, auch [q.e.d.]([[Q.E.D.]]), [[w.z.b.w.]], QED, ![image.png](../assets/image_1697192491775_0.png)logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Flogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Vlogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,212,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,215,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Hlogseq____&quot;,212,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Hlogseq____&quot;,215,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-9760-43f8-ab43-f6c5c0713fe3logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\logseq____&quot;\\\\text{x ist prim}\\logseq____&quot; \\\\quad logseq____&amp; \\\\text{ist AF mit Variablen x über den  natürlichen Zahlen}\\\\\\\\\\n\\logseq____&quot;\\\\underbrace{x}_{x_1}logseq____&lt;\\\\underbrace{y}_{x_2}\\logseq____&quot;\\\\quad logseq____&amp;\\\\text{ist AF mit Variablen }x,y\\\\text{ über die reellen Zahlen } \\\\underbrace{\\\\Reals}_{U_1},\\\\underbrace{\\\\Reals}_{U_2}\\\\\\\\\\n\\logseq____&quot;\\\\text{x ist wahr}\\logseq____&quot;\\\\quadlogseq____&amp;\\\\text{ist AF mit Variablen x über dem Universum der Aussagen}\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Flogseq____&quot;,252,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Vlogseq____&quot;,244,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-a6b8-4a80-b840-a75c6a133a71logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nlogseq____&amp;\\\\neg\\\\left(\\\\forall x :\\\\exists y :\\\\forall w :\\\\forall u :\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)\\\\right)\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x:(\\\\neg(\\\\exists y: \\\\forall w: \\\\forall u: \\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x:\\\\forall y:(\\\\neg(\\\\forall w: \\\\forall u:\\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x:\\\\forall y:\\\\exists w:(\\\\neg(\\\\forall u:\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x: \\\\forall y: \\\\exists w: \\\\exists u : \\\\forall z:\\\\neg(p(x,y,z)\\\\rightarrow q(u,w))\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Flogseq____&quot;,239,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Vlogseq____&quot;,239,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-b6f8-438d-95b0-e122f7deaa87logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nlogseq____&amp;\\\\forall x: \\\\forall y: p(x, y) \\\\equiv \\\\forall y: \\\\forall x: p(x,y)\\\\\\\\\\nlogseq____&amp;\\\\exists x:\\\\exists y:p(x,y)\\\\equiv\\\\exists y:\\\\exists x:p(x,y)\\\\\\\\\\nlogseq____&amp;[\\\\forall x_1:\\\\forall x_2: \\\\cdots:\\\\forall x_n:p(x_1,x_2,\\\\cdots,x_n)\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\equiv\\\\forall_{x_{\\\\pi(1)}}:\\\\forall_{x_{\\\\pi(1)}}:\\\\cdots:\\\\forall_{x_{\\\\pi(1)}}:p(x_1,x_2,\\\\cdots,x_n)\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Flogseq____&quot;,248,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Vlogseq____&quot;,248,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-4fbf-4a48-9ba2-d2fce807a8e5logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Aussageform]] (AF) über [Universen]([[Universen (Logik)]]) $U_1,\\\\cdots,U_n$: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;,244,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Vlogseq____&quot;,244,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Hlogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Hlogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-19a5-4587-87e5-b7aead08363flogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Regeln]]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;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Vlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Hlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^17logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-29da-4169-aea0-1f2b840d48c4logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Regeln]]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;,238,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Vlogseq____&quot;,244,536870923]],[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;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Hlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-bf17-461e-aff4-286d56eaf7f6logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;wobei $\\\\pi$ eine \\logseq____&quot;[[Permutation]]\\logseq____&quot; der Zahl $(1,2,\\\\cdots,n)$ istlogseq____&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;,256,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Vlogseq____&quot;,256,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Hlogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-3a75-4990-8cd6-b8a82bc24973logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Flogseq____&quot;,272,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Vlogseq____&quot;,272,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,230,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Hlogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Hlogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Hlogseq____&quot;,230,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-8bbe-4f4e-a679-86a1c8ccf6b3logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Wäre $y$ aus $\\\\Reals$ mit $xlogseq____&lt;y$ für alle $x$ aus $\\\\Reals$, so insbesondere auch $ylogseq____&lt;y$, Widerspruch. $\\\\blacksquare$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Flogseq____&quot;,245,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Vlogseq____&quot;,245,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-fea0-42a4-9142-f6aa1a30087elogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[263,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;,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Flogseq____&quot;,251,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Vlogseq____&quot;,251,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Hlogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-2de0-406b-ab99-c852859cee7clogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])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;,256,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Vlogseq____&quot;,248,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Hlogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-fa92-40b1-9f43-fad3770c90a2logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Für das leere Universum gilt\\n\\\\begin{align}\\n\\\\forall x: p(x)\\\\quadlogseq____&amp;Tautologie\\\\\\\\\\n\\\\exists x: p(x)\\\\quadlogseq____&amp;Kontradiktion\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Flogseq____&quot;,273,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Vlogseq____&quot;,244,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-c56f-426c-9a9d-9e259fe68241logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Endliches Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$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;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Vlogseq____&quot;,244,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-399a-44c4-80b4-a85a01e60e3alogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXMElogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Flogseq____&quot;,238,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Vlogseq____&quot;,238,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,42,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Hlogseq____&quot;,42,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-675f-4bbf-a78f-c046b9aca568logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Nach Ersetzung von $x$ in der AF $\\logseq____&quot;xlogseq____&lt;y\\logseq____&quot;$ durch eine konkrete Zahl entsteht eine AF in der Variablen $y$, z. Bsp. $\\logseq____&quot;17logseq____&lt;y\\logseq____&quot;$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Flogseq____&quot;,254,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Vlogseq____&quot;,254,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-b3d6-4d38-a95a-b9c0025fc729logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Verschiedene [[Quantoren]] dürfen **nicht** vertauscht werdenlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Flogseq____&quot;,260,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Vlogseq____&quot;,256,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Hlogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-c7e0-46a8-afa3-e1ffc82ca69elogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\underbrace{\\\\forall}_\\\\text{Allquantor} x: p(x) logseq____&amp;\\\\equiv p(O_1) \\\\land p(O_2) \\\\land \\\\cdots \\\\land p(O_m)\\\\\\\\\\n\\\\underbrace{\\\\exists}_\\\\text{Existenzquantor} x: p(x) logseq____&amp;\\\\equiv p(0_1) \\\\lor p(O_2) \\\\lor \\\\cdots \\\\lor p(0_m)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Flogseq____&quot;,266,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Vlogseq____&quot;,244,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-5ef2-4190-9b18-4930122279f2logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Allquantor]] [[Existenzquantor]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Flogseq____&quot;,270,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Vlogseq____&quot;,270,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Hlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Hlogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u652978da-0875-4684-b510-e07639365e7clogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[272,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 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beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der 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\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Flogseq____&quot;,102,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Vlogseq____&quot;,102,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,31,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-4c19-4f32-b4e0-1caab889c056logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Flogseq____&quot;,60,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Vlogseq____&quot;,51,536870919]],[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;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Hlogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-b3b0-405e-b17d-caededb226fblogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nax^2+bx+clogseq____&amp;=0logseq____&amp;|:a\\\\quadlogseq____&amp;a\\\\ne0\\\\\\\\\\nx^2+\\\\frac ba x + \\\\frac ca logseq____&amp;= 0\\\\\\\\\\nplogseq____&amp;=\\\\frac ba,logseq____&amp;q = \\\\frac ca\\\\\\\\\\nx^2+px+qlogseq____&amp;=0\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Flogseq____&quot;,69,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Vlogseq____&quot;,69,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-27a8-42a7-9b9e-1268c34d207clogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche }$[[Gleichungen]]$\\\\text{ sind richtig?}$\\n\\\\begin{align}\\ne^{x+y} logseq____&amp;= e^x + e^y logseq____&amp; ,f \\\\\\\\\\ne^{x+y} logseq____&amp;= e^x * x^y logseq____&amp; ,r \\\\\\\\\\ne^{x+y}logseq____&amp;=e^{xy} logseq____&amp; ,f\\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=x+y logseq____&amp; ,x+ylogseq____&gt;c \\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=e^x*e^ylogseq____&amp;,f\\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=ln(e^x+y)logseq____&amp;,x+ylogseq____&gt;0\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Flogseq____&quot;,83,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Vlogseq____&quot;,83,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,33,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Hlogseq____&quot;,33,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-69c4-48bb-8e4b-728e16cf92a3logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____&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;,68,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Vlogseq____&quot;,68,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,32,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,38,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Hlogseq____&quot;,38,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-b09c-4646-842a-8bb47fdd9047logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Rationalmachen]] des [[Nenner]]slogseq____&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;,98,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Vlogseq____&quot;,92,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Hlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Hlogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-3af4-43bd-81b5-1e0139bd2c2blogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Wenn }alogseq____&gt;0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac b{\\\\sqrt a} = \\\\frac b{\\\\sqrt a}*\\\\frac{\\\\sqrt a}{\\\\sqrt a} = \\\\frac {b\\\\sqrt a}a\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[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;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Vlogseq____&quot;,77,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-eb5b-42f8-8b70-c6d2360e4a58logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Potenzen]] und [[Wurzeln]]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;,86,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Hlogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Hlogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-a4d9-4dbd-94f1-346c7d2e77a5logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Für } x=\\\\frac25 \\\\text{ und } y=\\\\frac37 \\\\text{ ist }\\\\frac xy$\\n\\\\begin{align}\\n\\\\frac xy = \\\\frac{\\\\frac25}{\\\\frac37} = \\\\frac{2*7}{3*5}=\\\\frac{14}{15}\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Flogseq____&quot;,82,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Vlogseq____&quot;,82,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-875b-4f23-a929-fa6a1d527566logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])\\n\\\\begin{align}\\nx^4-34x^2+225logseq____&amp;=0\\\\\\\\\\n\\\\text{substituiert }ylogseq____&amp;=x^2\\\\\\\\\\ny^2-34y+225logseq____&amp;=0\\\\\\\\\\ny_{1,2}logseq____&amp;=17\\\\pm\\\\sqrt{(-17)^2-225}\\\\\\\\\\nlogseq____&amp;=17\\\\pm\\\\sqrt{289-225}\\nlogseq____&amp;=17\\\\pm\\\\sqrt{64}=17\\\\pm8\\\\\\\\\\nlogseq____&amp;=\\\\left.\\\\begin{cases}\\n25\\\\\\\\\\n9\\n\\\\end{cases}\\\\right|\\\\begin{array}{l}\\nx^2=25logseq____&amp;\\\\rightarrow logseq____&amp;x_1=5;logseq____&amp;x_2=-5\\\\\\\\\\nx^2=9logseq____&amp;\\\\rightarrow logseq____&amp;x_1=3;logseq____&amp;x_2=-3\\\\\\\\\\n\\\\end{array}\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Flogseq____&quot;,63,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Vlogseq____&quot;,88,536870919]],[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;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Hlogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-0da5-4ef6-bf0f-cc19eb8ccf38logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Was ist Größer?logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Flogseq____&quot;,95,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-d747-41a0-acaf-2b75d6d668b8logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Potenzen]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Flogseq____&quot;,64,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Hlogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-9cf9-4f21-9d83-44083342d912logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche quadratische Gleichung hat die Lösung}$\\n$x_1=3\\\\quad x_2=4$\\n\\\\begin{align}\\nx_1+x_2 = 7 logseq____&amp;= p logseq____&amp;, 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[[Binomische Formeln]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Flogseq____&quot;,47,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Wurzeln]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Flogseq____&quot;,102,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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a + \\\\ln b logseq____&amp;= \\\\ln(a*b) \\\\\\\\\\n\\\\ln(-a) logseq____&amp;= \\\\frac1{\\\\ln 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Lösung von } x^n-a=0 \\\\text{ ist } x=\\\\sqrt[n]a$ #FIXME ich glaube hier fehlt logseq____&gt;0 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Lösung mit 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2}\\\\quad 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3}\\\\quad xlogseq____&gt;3$\\n\\\\begin{align}\\nx+5logseq____&amp;logseq____&gt;0\\\\\\\\\\n|x+5|logseq____&amp;=x+5\\\\\\\\\\nx-3logseq____&amp;\\\\ge0\\\\\\\\\\n|x-3|logseq____&amp;=x-3\\\\\\\\\\nx+5logseq____&amp;logseq____&lt;2(x-3)\\\\\\\\\\nx+5logseq____&amp;logseq____&lt;2x-3 logseq____&amp;|logseq____&amp; -2x-5\\\\\\\\\\n-xlogseq____&amp;logseq____&lt;-11 logseq____&amp;|logseq____&amp; 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Lösung mit 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$\\\\rightarrow$ 5 ist abstand von x zu 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Meinel, M. Mundhenk,  [[\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. Auflage 2011]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Flogseq____&quot;,185,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Vlogseq____&quot;,185,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Hlogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-849e-4928-bde2-82854231b06alogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\nlogseq____&amp;\\logseq____&quot;5\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;\\\\quadlogseq____&amp; (w)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;4\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;logseq____&amp; (f)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Jede gerade Zahl }\\\\ge4\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ ist Summe zweier Primzahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage, }w\\\\text{ oder }f)\\\\notag\\\\\\\\\\nlogseq____&amp;(\\\\text{Vermutung von Goldback 1742})\\\\text{, }logseq____&amp;logseq____&amp;\\\\text{richtig für gerade Zahlen bis }4*10^{18}\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Dieser Satz ist falsch}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{keine Aussage})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Gleichung } x^2+y^2=z^2 \\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ hat eine Lösung }x,y,z\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nlogseq____&amp;x^n+y^n=z^n\\\\text{ eine Lösung}logseq____&amp;logseq____&amp; (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nlogseq____&amp;x,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp;\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Gott ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Nietzsche ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Flogseq____&quot;,201,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Vlogseq____&quot;,205,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-cc56-4a2c-bf3c-c6804f172ea2logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Variable]([[Variablen]]), die den Wert $w$ oder $f$ annimmtlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Flogseq____&quot;,193,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Vlogseq____&quot;,193,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,163,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Hlogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-98a4-4f22-9851-5fd0c64f3a34logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Büchertiplogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Flogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Vlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^17logseq____&quot;,false,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-792a-4028-9f0f-ef217b2d3015logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[186,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;,[186,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Flogseq____&quot;,181,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Vlogseq____&quot;,203,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,172,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,179,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Hlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Hlogseq____&quot;,172,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Hlogseq____&quot;,179,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-180b-45d3-ba12-93e5483430fflogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $w$ istlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Flogseq____&quot;,199,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Vlogseq____&quot;,199,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-b7b3-4e15-8884-823d763d7a6alogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Zuordnung von $w/f$ an jede [Variable]([[Variablen]]) einer [[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Flogseq____&quot;,204,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Vlogseq____&quot;,204,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Hlogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Hlogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-d714-4e5d-bb9f-31d47ef03ea3logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Flogseq____&quot;,207,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Vlogseq____&quot;,207,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,42,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,175,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Hlogseq____&quot;,42,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Hlogseq____&quot;,175,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-53fa-4949-a893-b1b37bb29a30logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Flogseq____&quot;,206,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Vlogseq____&quot;,206,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Hlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Hlogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Hlogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Hlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-d1da-422c-ad41-accc2a151473logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Weitere [[Beispiele]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Flogseq____&quot;,200,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Vlogseq____&quot;,203,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Hlogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-e3ac-46aa-acd7-115000ebe5bdlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sind $p$ und $q$ [[Aussagen]], so auch\\n\\\\begin{align}\\n(p\\\\land q) logseq____&amp;\\\\quadlogseq____&amp; (\\logseq____&quot;\\\\text{und}\\logseq____&quot;)\\\\\\\\\\n(p\\\\lor q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{oder}\\logseq____&quot;)\\\\\\\\\\n(\\\\neg p) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{nicht}\\logseq____&quot;)\\\\\\\\\\n(p\\\\rightarrow q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{impliziert}\\logseq____&quot;)\\\\\\\\\\n(p\\\\leftrightarrow q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{genau dann wenn}\\logseq____&quot;)\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Flogseq____&quot;,203,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Vlogseq____&quot;,203,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Hlogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-6200-471b-aa20-26bc2cdb3d2flogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussagenlogische Variable]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Flogseq____&quot;,197,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Vlogseq____&quot;,203,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,163,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Hlogseq____&quot;,163,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-ac30-4275-b950-deced5149d8clogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Flogseq____&quot;,192,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Vlogseq____&quot;,203,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Hlogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-0e9b-42cf-9cec-0c98204709b3logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wikipedia]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Flogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Vlogseq____&quot;,185,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,164,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Hlogseq____&quot;,164,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-9a8f-4d41-80aa-f0d5036d134dlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[196,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;,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Flogseq____&quot;,191,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Vlogseq____&quot;,191,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-9daf-4698-99ee-daabfe1e5c63logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Soweit die \\logseq____&quot;[[Syntax]]\\logseq____&quot;, jetzt die [[Semantik]]. Die [Wahrheitswerte]([[Wahrheitswert]])\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Flogseq____&quot;,194,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Vlogseq____&quot;,203,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,171,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,177,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Hlogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Hlogseq____&quot;,171,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Hlogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Hlogseq____&quot;,177,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-ef94-4e9e-b6b3-fbea84f0c9c5logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[198,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;,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Flogseq____&quot;,194,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Vlogseq____&quot;,194,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-7b4b-46f8-af57-038e0b188380logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Tantologie]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Flogseq____&quot;,206,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Vlogseq____&quot;,203,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Hlogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-1820-4e26-9138-140ca22fb754logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Flogseq____&quot;,186,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Vlogseq____&quot;,203,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Hlogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-f053-404f-a517-43dcaf0460c8logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[201,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;,[201,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Flogseq____&quot;,205,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Vlogseq____&quot;,205,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Hlogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-97cc-485f-a35b-4621df6372celogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $f$ istlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Flogseq____&quot;,181,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Vlogseq____&quot;,181,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,169,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-d93a-4fc1-bc02-6477478a771flogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Verknüpfung von Aussagen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Flogseq____&quot;,183,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Vlogseq____&quot;,205,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Hlogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297970-45d8-491a-b8d0-70d1bda3748dlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Belegung]] (der [[Variablen]])logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Flogseq____&quot;,207,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Vlogseq____&quot;,203,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Aussagen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Flogseq____&quot;,185,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Vlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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mit [[Variablen]] $x_1,\\\\cdots,x_n$, der bei Ersetzung jedes $x_j$ durch ein [Objekt]([[Objekt (Logik)]]) aus $U_j$ stets zu einer [Aussage]([[Aussagen]]) wirdlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Flogseq____&quot;,245,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Vlogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,170,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,174,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,231,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Hlogseq____&quot;,170,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Hlogseq____&quot;,174,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Hlogseq____&quot;,231,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Hlogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-f334-45e8-8f54-c22f77cd81delogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\logseq____&quot;\\\\text{x ist prim}\\logseq____&quot; \\\\quad logseq____&amp; \\\\text{ist AF mit Variablen x über den  natürlichen Zahlen}\\\\\\\\\\n\\logseq____&quot;\\\\underbrace{x}_{x_1}logseq____&lt;\\\\underbrace{y}_{x_2}\\logseq____&quot;\\\\quad logseq____&amp;\\\\text{ist AF mit Variablen }x,y\\\\text{ über die reellen Zahlen } \\\\underbrace{\\\\Reals}_{U_1},\\\\underbrace{\\\\Reals}_{U_2}\\\\\\\\\\n\\logseq____&quot;\\\\text{x ist wahr}\\logseq____&quot;\\\\quadlogseq____&amp;\\\\text{ist AF mit Variablen x über dem Universum der Aussagen}\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Flogseq____&quot;,246,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Vlogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-e6a0-44f6-8b7c-7fff2455582elogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nlogseq____&amp;\\\\forall x: \\\\forall y: p(x, y) \\\\equiv \\\\forall y: \\\\forall x: p(x,y)\\\\\\\\\\nlogseq____&amp;\\\\exists x:\\\\exists y:p(x,y)\\\\equiv\\\\exists y:\\\\exists x:p(x,y)\\\\\\\\\\nlogseq____&amp;[\\\\forall x_1:\\\\forall x_2: \\\\cdots:\\\\forall x_n:p(x_1,x_2,\\\\cdots,x_n)\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\equiv\\\\forall_{x_{\\\\pi(1)}}:\\\\forall_{x_{\\\\pi(1)}}:\\\\cdots:\\\\forall_{x_{\\\\pi(1)}}:p(x_1,x_2,\\\\cdots,x_n)\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Flogseq____&quot;,256,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Vlogseq____&quot;,256,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-16e4-4cb6-a013-6740f2997e2blogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;wobei $\\\\pi$ eine \\logseq____&quot;[[Permutation]]\\logseq____&quot; der Zahl $(1,2,\\\\cdots,n)$ 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;,242,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Vlogseq____&quot;,242,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Hlogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-472d-4e56-9809-3c3e93a0d867logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\underbrace{\\\\forall}_\\\\text{Allquantor} x: p(x) logseq____&amp;\\\\equiv p(O_1) \\\\land p(O_2) \\\\land \\\\cdots \\\\land p(O_m)\\\\\\\\\\n\\\\underbrace{\\\\exists}_\\\\text{Existenzquantor} x: p(x) logseq____&amp;\\\\equiv p(0_1) \\\\lor p(O_2) \\\\lor \\\\cdots \\\\lor p(0_m)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Flogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Vlogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-e965-42e8-9597-481319ec110blogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Aussageform]] (AF) über [Universen]([[Universen (Logik)]]) $U_1,\\\\cdots,U_n$:logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Flogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Vlogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Hlogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Hlogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-400a-486f-8b33-60f9eda7c8cdlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Flogseq____&quot;,240,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Vlogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Hlogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-57e8-424c-bda3-acd46b235e2dlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Regeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Flogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Vlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Allquantor]] [[Existenzquantor]]logseq____&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;,244,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Vlogseq____&quot;,244,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Hlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Hlogseq____&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;~u65297971-5d07-414a-8263-f309f76ac18dlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\exists 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[[Regeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Flogseq____&quot;,262,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Vlogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Hlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-416e-4467-b045-d478d7e3df9alogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Widerspruch = ↯, 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[[Quantoren]] dürfen vertauscht 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x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist 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$p(x)$ AF in der Variablen $x$ über $U$: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;,241,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Vlogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-0231-4c42-9bc7-60b10c2f2ae1logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Für das leere Universum gilt\\n\\\\begin{align}\\n\\\\forall x: p(x)\\\\quadlogseq____&amp;Tautologie\\\\\\\\\\n\\\\exists x: p(x)\\\\quadlogseq____&amp;Kontradiktion\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Flogseq____&quot;,238,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Vlogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&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;~u65297971-671f-4d52-8cfd-2bd0c373c26dlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:(p(x)\\\\land q(x)) logseq____&amp;\\\\equiv (\\\\forall x: p(x)) \\\\land (\\\\forall x:q(x));\\\\notag\\\\\\\\\\n\\\\exists x: (p(x) \\\\lor q(x)) logseq____&amp;\\\\equiv (\\\\exists x: p(x))\\\\lor(\\\\exists x: q(x)),\\\\quadlogseq____&amp;\\\\text{Große Assoziativgesetze}\\\\\\\\\\n\\\\neg(\\\\forall x:p(x))logseq____&amp;\\\\equiv \\\\exists x: (\\\\neg p(x));\\\\quadlogseq____&amp;\\\\text{Große de Morgansche Regeln;}\\\\notag\\\\\\\\\\n\\\\neg(\\\\exists x: p(x)) logseq____&amp;\\\\equiv \\\\forall x: (\\\\neg p(x)),\\\\quadlogseq____&amp;\\\\text{Negationsregeln.}\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Flogseq____&quot;,254,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Vlogseq____&quot;,254,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-073c-4ff2-b877-2b476f721447logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Nach Ersetzung von $x$ in der AF $\\logseq____&quot;xlogseq____&lt;y\\logseq____&quot;$ durch eine konkrete Zahl entsteht eine AF in der Variablen $y$, z. Bsp. $\\logseq____&quot;17logseq____&lt;y\\logseq____&quot;$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[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;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Vlogseq____&quot;,241,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-842c-4979-9d5a-cad64896b7b1logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativschreibweisen:\\n$\\\\forall x: p(x)$ auch $\\\\bigwedge x:p(x)$\\n$\\\\exists x:p(x)$ auch $\\\\bigvee 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mit Objekten $O_1,\\\\cdots,O_m$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;,259,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Vlogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-e130-440b-8eab-cefad239ce2dlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])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;,242,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Vlogseq____&quot;,256,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Hlogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-e7f5-4271-b14a-9d4873f3f9d8logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x,y)$ AF in Variablen $x,y$ über $U_1,U_2$\\n\\\\begin{align}\\n\\\\underbrace{\\\\forall x: \\\\underbrace{\\\\exists y: p(x,y)}_{\\\\text{AF in den Variablen }x\\\\text{ über }U_1}}_{\\\\text{Aussage}}\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Flogseq____&quot;,250,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Vlogseq____&quot;,250,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-e1ce-4996-9a83-5a5f7bff7a96logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $x$ aus $\\\\Reals$ beliebig. Setze $y:=x+1$ (ist aus $\\\\Reals$). Dann ist $xlogseq____&lt;x+1=y$ also $xlogseq____&lt;y$. $\\\\blacksquare$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Flogseq____&quot;,271,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Vlogseq____&quot;,271,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-f106-4b75-ba5a-548c292537c4logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Verschiedene [[Quantoren]] dürfen **nicht** vertauscht werdenlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Flogseq____&quot;,243,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Vlogseq____&quot;,242,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Hlogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-740d-4f0a-929d-8203ff0cc72clogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche Regeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Flogseq____&quot;,270,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Vlogseq____&quot;,270,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,211,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,219,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,226,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Hlogseq____&quot;,211,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Hlogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Hlogseq____&quot;,219,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Hlogseq____&quot;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Hlogseq____&quot;,226,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Hlogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-4727-4fc8-a328-ae913737c480logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Wäre $y$ aus $\\\\Reals$ mit $xlogseq____&lt;y$ für alle $x$ aus $\\\\Reals$, so insbesondere auch $ylogseq____&lt;y$, Widerspruch. $\\\\blacksquare$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Flogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Vlogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-fa98-4944-a224-3f54da9bb6c6logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n(p\\\\land q)\\\\land r logseq____&amp;\\\\equiv p\\\\land(q\\\\land r),\\\\quadlogseq____&amp;\\\\text{schreibe daher: }  p\\\\land q\\\\land r,\\\\quad \\\\land \\\\text{ assoziativ}\\\\\\\\\\n(p \\\\lor q) \\\\lor r logseq____&amp;\\\\equiv p \\\\lor (q\\\\lor r),\\\\quadlogseq____&amp;\\\\text{schreibe daher: } p\\\\lor q\\\\lor r,\\\\quad \\\\lor \\\\text{ assoziativ}\\\\\\\\\\np \\\\land q logseq____&amp;\\\\equiv q \\\\land p,\\\\quad \\\\land logseq____&amp;\\\\text{ kommutativ}\\\\\\\\\\np \\\\lor q logseq____&amp;\\\\equiv q \\\\lor p,\\\\quad \\\\lor logseq____&amp;\\\\text{ kommutativ}\\\\\\\\\\n\\\\neg(\\\\neg p) logseq____&amp;\\\\equiv p, \\\\quad \\\\neg logseq____&amp;\\\\text{ idenpotent}\\\\\\\\\\np\\\\land(q\\\\lor r)logseq____&amp;\\\\equiv (p\\\\land q)\\\\lor(p\\\\land r);\\\\notag\\\\\\\\\\np\\\\lor(q\\\\land r)logseq____&amp;\\\\equiv (p\\\\lor q)\\\\lor(p\\\\land r),\\\\quad logseq____&amp;\\\\land,\\\\lor\\\\text{ wechselseitig distributiv}\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&amp;\\\\equiv(\\\\neg p)\\\\lor(\\\\neg q);\\\\notag\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&amp;\\\\equiv(\\\\neg p)\\\\land (\\\\neg q), \\\\quad logseq____&amp;\\\\text{ (kleine) de Morgansche Regeln}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Flogseq____&quot;,247,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Vlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-4cf4-4f2f-a8de-e11adf2951a1logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[271,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;,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Flogseq____&quot;,236,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Vlogseq____&quot;,236,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Hlogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-c908-4418-ba1d-2fc164d4307flogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\forall x:p(x)$ ist die [Aussage]([[[]Aussagen]]): $\\logseq____&quot;\\\\text{Für alle x aus U ist p(x) wahr}\\logseq____&quot;\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w\\\\quadlogseq____&amp;\\\\text{fallls p(x) w für alle x aus U}\\\\\\\\f\\\\quadlogseq____&amp;\\\\text{falls p(x) f für (wenigstens) ein x aus U}\\\\end{cases}$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Flogseq____&quot;,258,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Vlogseq____&quot;,258,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Ulogseq____&quot;,166,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Ulogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Hlogseq____&quot;,166,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Hlogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297971-4b64-4425-b100-5c11803b1fe7logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] 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