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[[Nenner]]slogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Flogseq____&quot;,80,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Vlogseq____&quot;,69,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Quadratische Gleichungen]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Flogseq____&quot;,69,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Vlogseq____&quot;,74,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Wurzeln]]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;,58,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[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;^?logseq____&quot;,[logseq____&quot;^ 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Wissensabgleich [[Logarithmen]]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;,89,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,31,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Hlogseq____&quot;,31,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c00-3d72-40f4-ad65-f3269df1ec8flogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____&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;,70,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Vlogseq____&quot;,70,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,32,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,38,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Hlogseq____&quot;,38,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c00-bf13-4978-9bae-65147cfc9deblogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[86,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;,[86,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Flogseq____&quot;,84,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Vlogseq____&quot;,84,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,31,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c00-dc4b-41f0-b440-701c0a99f406logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel für die 3. Binomische Formel}$\\n\\\\begin{align}\\n\\\\frac{\\\\frac1{a-b}+\\\\frac1{a+b}}{\\\\frac1{a-b}-\\\\frac1{a+b}}\\nlogseq____&amp;=\\\\frac{\\\\frac{a+b+a-b}{(a+b)*(a-b)}}{\\\\frac{a+b-(a-b)}{(a+b)*(a-b)}}\\nlogseq____&amp;=\\\\frac{a+b+a-b}{a+b-a+b}\\nlogseq____&amp;=\\\\frac{2a}{2b}\\nlogseq____&amp;=\\\\frac ab\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Flogseq____&quot;,82,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Vlogseq____&quot;,58,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[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;~u65296c00-8cc0-47a9-abd0-2b2b9d906511logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]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;,51,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Vlogseq____&quot;,69,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Hlogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c00-2664-421d-a20a-d99fb034a10blogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Potenzen]]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;,99,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Hlogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c00-74a1-4210-bd81-2367ca4df40elogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[90,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;,[90,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Flogseq____&quot;,53,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Vlogseq____&quot;,89,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c00-1ad5-4e8a-b4c4-ea1e8f22b5ealogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[91,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;,[91,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Flogseq____&quot;,92,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Vlogseq____&quot;,92,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,26,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Hlogseq____&quot;,26,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c00-758f-4bbd-afce-ebd09b617fb6logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[pq-Formel]]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;,100,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Vlogseq____&quot;,56,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Hlogseq____&quot;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c00-8055-4b40-b5b6-c6ed0710aa06logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Wurzeln]]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;,84,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Hlogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c00-94f6-495e-ae4e-54ec123fb6c6logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n(a+b)^3(a^2+b^2)^3(a-b)^3logseq____&amp;=(a^2+b^2)^3\\\\left((a+b)(a-b)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=(a^2+b^2)^3(a^2-b^2)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=\\\\left((a^2+b^2)(a^2-b^2)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=(a^4-b^4)^3\\\\\\\\\\n\\\\frac{a-b}{(a+b)^{-1}}logseq____&amp;=(a-b)(a+b)\\\\notag\\\\\\\\\\nlogseq____&amp;=a^2-b^2\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Flogseq____&quot;,76,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Vlogseq____&quot;,76,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c00-319e-4936-9b39-c74287bcbaa0logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\n\\\\tan x logseq____&amp;= \\\\frac{\\\\sin x}{\\\\cos x} logseq____&amp;, \\\\cos x \\\\ne 0\\\\\\\\\\n\\\\sin^{-2}x-\\\\cos^2xlogseq____&amp;=1logseq____&amp;,f\\\\\\\\\\n\\\\sin x = \\\\cos x logseq____&amp;= 1 logseq____&amp;, f\\\\\\\\\\n\\\\sin^{-2}x+cos^2ylogseq____&amp;=1logseq____&amp;,r\\\\\\\\\\n1+tan^2xlogseq____&amp;=\\\\frac1{\\\\cos^2x}logseq____&amp;,\\\\cos x\\\\ne0\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Flogseq____&quot;,60,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Vlogseq____&quot;,104,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c00-2d56-456d-aa23-f595821400fdlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\underbrace{\\\\frac6{2+\\\\sqrt2}*\\\\frac{2-\\\\sqrt2}{2-\\\\sqrt2}\\n= 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Lösung mit 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Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Flogseq____&quot;,142,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Vlogseq____&quot;,142,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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aller rellen Zahlen zwischen 4 und $\\\\infty$ ohne 4 und $\\\\infty$\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|xlogseq____&gt;4\\\\right\\\\}=:(4,\\\\infty)\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Flogseq____&quot;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Vlogseq____&quot;,138,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[149,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c00-c3db-4724-9ac3-a27f1c8fe503logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Flogseq____&quot;,146,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Vlogseq____&quot;,146,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Jlogseq____&quot;,[],536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^Hlogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[150,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c00-5f1a-487c-9473-54d76c17f1b8logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 2}\\\\quad -5\\\\le xlogseq____&lt;3$\\n\\\\begin{align}\\nx+5logseq____&amp;\\\\le0\\\\\\\\\\n|x+5|logseq____&amp;=x+5\\\\\\\\\\nx-3logseq____&amp;logseq____&lt;0\\\\\\\\\\n|x-3|logseq____&amp;=-(x-3)=-x+3\\\\\\\\\\nx+5logseq____&amp;logseq____&lt;2(-x+3)\\\\\\\\\\nx+5logseq____&amp;logseq____&lt;-2x+6 logseq____&amp;|logseq____&amp;+2x\\\\\\\\\\n3xlogseq____&amp;logseq____&lt;1 logseq____&amp;|logseq____&amp; :3\\\\\\\\\\nxlogseq____&amp;logseq____&lt;\\\\frac13\\n\\\\end{align}\\n\\\\begin{align}\\nL_2=\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-5\\\\le xlogseq____&lt;3,xlogseq____&lt;\\\\frac13\\\\right\\\\}\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Flogseq____&quot;,148,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Vlogseq____&quot;,122,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[151,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c00-9fb1-4910-98d8-a6fe4b5de5a7logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Der [[Betrag]] ist der [[Abstand]] zu 0\\n\\\\begin{align}\\nf(x)=logseq____&amp;|x|:=logseq____&amp;\\\\begin{cases}\\nxlogseq____&amp;x\\\\ge0\\\\\\\\\\n-xlogseq____&amp;xlogseq____&lt;0\\n\\\\end{cases}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Flogseq____&quot;,133,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Vlogseq____&quot;,133,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Ulogseq____&quot;,110,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Hlogseq____&quot;,110,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^Hlogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c00-904f-4f04-bc47-c79b9d50e9c9logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 1}\\\\quad x\\\\ge3$\\n\\\\begin{align}\\n|x-3|logseq____&amp;=x-3\\\\\\\\\\nx-3\\\\le|x+2|\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Flogseq____&quot;,116,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Vlogseq____&quot;,116,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[153,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c00-6e21-43a9-8908-e04e838722celogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[154,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Kombinieren:\\n\\\\begin{align}\\nL=L_1\\\\cup 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aller reellen Zahlen zwischen 1 und 4 inklusive 1 und 4\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-1\\\\le x\\\\le4\\\\right\\\\}=:\\\\underbrace{[-1,4]}_\\\\text{Abgeschlossenes 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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;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-5a02-4800-8f3e-528a6d2d8664logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[184,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;,[184,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Flogseq____&quot;,199,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Vlogseq____&quot;,199,536870922]],[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;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-49a4-4960-994c-93202e81181dlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussagenlogische Variable]]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;,199,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,163,536870922]],[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;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Hlogseq____&quot;,163,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-0bbe-4f88-b7fd-3a47bfaf2fd6logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[186,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;,[186,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Flogseq____&quot;,189,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Vlogseq____&quot;,188,536870922]],[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;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Hlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-54ec-4750-a97c-a5e2eeb426ddlogseq____&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;,183,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Vlogseq____&quot;,183,536870922]],[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;~u65296c01-ab5c-467f-967b-017834a64163logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Wahrheitswerteverlauf]] 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;,181,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Vlogseq____&quot;,199,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Hlogseq____&quot;,162,536870922]],[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;~u65296c01-548a-4150-8bac-d2c240ebe5e1logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])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;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[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;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Hlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Hlogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Hlogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Hlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-fba1-4d2e-9f4f-610855cbcad0logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[190,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;,[190,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Flogseq____&quot;,203,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Vlogseq____&quot;,203,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-5cac-4b1d-acf4-7d4590b61517logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Zuordnung von $w/f$ an jede [Variable]([[Variablen]]) einer [[Aussageformel]]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;,181,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Vlogseq____&quot;,181,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Hlogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Hlogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-b5c5-4098-8ba7-82773668653elogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[192,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;,[192,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Flogseq____&quot;,194,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Vlogseq____&quot;,199,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,172,536870922]],[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;^Ulogseq____&quot;,179,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Hlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Hlogseq____&quot;,172,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Hlogseq____&quot;,179,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-2fa2-448d-aa8f-0a65649654c0logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____&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;,206,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Vlogseq____&quot;,206,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,42,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,175,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Hlogseq____&quot;,42,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Hlogseq____&quot;,175,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-1aee-4c36-88fe-1af47742096flogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Kontradiktion]]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;,183,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Vlogseq____&quot;,199,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,169,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Hlogseq____&quot;,169,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-0711-4c2c-b2a4-e835a64068c2logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[195,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;,[195,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Flogseq____&quot;,202,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Vlogseq____&quot;,202,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Hlogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-1b21-41da-8cdb-b24b21cbd49blogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Flogseq____&quot;,192,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Vlogseq____&quot;,199,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,168,536870922]],[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;^Hlogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-8bfc-4f2f-87ac-3f7c5f68295alogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[197,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;,[197,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Flogseq____&quot;,198,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Vlogseq____&quot;,198,536870922]],[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;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Hlogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-00eb-4f58-bfa7-363e146aa5c9logseq____&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;,202,536870922]],[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;~u65296c01-2c8a-45e1-ac7b-e4afd146359blogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Verknüpfung von Aussagen]]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;,207,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Vlogseq____&quot;,198,536870922]],[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;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Hlogseq____&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;~u65296c01-8563-428d-9bf8-43218c35235dlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[200,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;,[200,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Flogseq____&quot;,203,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Vlogseq____&quot;,199,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,171,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,177,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Hlogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Hlogseq____&quot;,171,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Hlogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Hlogseq____&quot;,177,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-23c0-4299-aca1-ef0c718fc416logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[201,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;,[201,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Flogseq____&quot;,208,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Vlogseq____&quot;,208,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-bf00-4033-ad12-c72f25ce34fclogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Büchertiplogseq____&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;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Vlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^17logseq____&quot;,false,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-d015-4078-8ae8-dfabd7b451f3logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]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;,184,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Vlogseq____&quot;,199,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,35,536870922]],[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;^Hlogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-c4be-4871-b5f6-2db286690475logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $f$ 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[[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Flogseq____&quot;,185,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Vlogseq____&quot;,199,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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#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;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[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;~u65296c01-c01f-4353-b08b-9d713ccb11felogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]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;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Vlogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ulogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ulogseq____&quot;,230,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Hlogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Hlogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Hlogseq____&quot;,230,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-06ca-47f7-8032-52544663b7f2logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[240,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;,[240,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Flogseq____&quot;,259,536870923]],[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;^Hlogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-5141-45b0-974c-b16c6e730b00logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Endliches Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$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;,258,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Vlogseq____&quot;,254,536870923]],[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;~u65296c01-8451-4323-93b8-365a347e8720logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x)$ AF in der Variablen $x$ über $U$: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;,266,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Vlogseq____&quot;,254,536870923]],[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;~u65296c01-e42c-4604-9e25-d989d5929b63logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche Regeln]]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;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Vlogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,211,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,219,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,226,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Hlogseq____&quot;,211,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Hlogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Hlogseq____&quot;,219,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Hlogseq____&quot;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Hlogseq____&quot;,226,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Hlogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-5488-4c77-96f4-8e0a81f0a455logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,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;,[244,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Flogseq____&quot;,269,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Vlogseq____&quot;,269,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[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;~u65296c01-3087-4ea7-a03d-973d6c1250c6logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,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;,[245,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Flogseq____&quot;,259,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Vlogseq____&quot;,259,536870923]],[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;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-f3b0-4497-84f4-23b14ce25f94logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,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;,[246,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Flogseq____&quot;,241,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Vlogseq____&quot;,254,536870923]],[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;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-3f31-4b98-929e-17f21cd72d43logseq____&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;,250,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Vlogseq____&quot;,254,536870923]],[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;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Hlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-1ef9-4e6a-ad58-26f9556d44cflogseq____&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;,247,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Vlogseq____&quot;,254,536870923]],[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;~u65296c01-d25b-49f2-aa18-baaac2b3adf9logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[249,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;,[249,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Flogseq____&quot;,273,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Vlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-f2ae-4339-8f1a-980268c9eb19logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[250,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;,[250,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Flogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Vlogseq____&quot;,254,536870923]],[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;~u65296c01-a198-4553-b650-10365f430b07logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Schachtelung von quantoren ([Beispiel]([[Beispiele]])):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;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Vlogseq____&quot;,247,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Hlogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-1ec8-4db5-9201-d0c828d19945logseq____&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;,261,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Vlogseq____&quot;,254,536870923]],[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;~u65296c01-2fd8-4e1e-929a-954debdd5c7dlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Allquantor]] [[Existenzquantor]]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;,246,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Vlogseq____&quot;,246,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Hlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Hlogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-dc69-4ee2-8a08-30fa96daca85logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Aussageform]]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;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Vlogseq____&quot;,217,536870923]],[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;,1],536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Hlogseq____&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;~u65296c01-e801-439a-b488-ebebe700a48clogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Die beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der [[Aussagenlogik]]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;,242,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Vlogseq____&quot;,254,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,214,536870923]],[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;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Hlogseq____&quot;,214,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Hlogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-a694-47e1-acc3-ac23911ed431logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Aussageform]] (AF) über [Universen]([[Universen (Logik)]]) $U_1,\\\\cdots,U_n$: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;,254,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Vlogseq____&quot;,254,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Hlogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Hlogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-544e-4921-a5bc-d6c2484fd095logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])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;,260,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Vlogseq____&quot;,248,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Hlogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-4354-4a9d-a7fa-2612a6900e59logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[258,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;,[258,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Flogseq____&quot;,255,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Vlogseq____&quot;,254,536870923]],[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;~u65296c01-64a8-4e44-b17f-059ffeed7f73logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist 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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;,[260,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Flogseq____&quot;,248,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Vlogseq____&quot;,248,536870923]],[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;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-4d53-475e-a843-f31dce40b23flogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[261,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;,[261,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Flogseq____&quot;,256,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Vlogseq____&quot;,254,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,170,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,174,536870923]],[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;^Ulogseq____&quot;,231,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Hlogseq____&quot;,170,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Hlogseq____&quot;,174,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Hlogseq____&quot;,231,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Hlogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-e73b-4b7f-872e-fdacad56bea4logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[262,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;,[262,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Flogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Vlogseq____&quot;,257,536870923]],[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;,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;~u65296c01-7a4d-4acf-b578-06c60d4dfe33logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[263,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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$\\\\pi$ eine \\logseq____&quot;[[Permutation]]\\logseq____&quot; der Zahl $(1,2,\\\\cdots,n)$ istlogseq____&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;,260,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Vlogseq____&quot;,260,536870923]],[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;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Hlogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-0633-40db-8515-202ee15c9372logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,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;,[265,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Flogseq____&quot;,240,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Vlogseq____&quot;,240,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[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;~u65296c01-eb80-4036-9dc2-51365faa6928logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[266,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;,[266,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Flogseq____&quot;,252,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Vlogseq____&quot;,254,536870923]],[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;~u65296c01-8ad2-4168-b480-0a8d7ae31e58logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[267,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;,[267,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Flogseq____&quot;,242,536870923]],[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;,166,536870923]],[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;^Ulogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Hlogseq____&quot;,166,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Hlogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65296c01-47aa-4c7e-8eba-e4b947a50ee3logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\blacksquare$ = Beweisende, auch [q.e.d.]([[Q.E.D.]]), [[w.z.b.w.]], QED, 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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;,[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;,266,536870923]],[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;~u65296c01-aec6-4000-b0f0-3260062783b3logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Verschiedene [[Quantoren]] dürfen **nicht** vertauscht 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// This script checks to see if a redirect is present in the query string
// and converts it back into the correct url and adds it to the
// browser's history using window.history.replaceState(...),
// which won't cause the browser to attempt to load the new url.
// When the single page app is loaded further down in this file,
// the correct url will be waiting in the browser's history for
// the single page app to route accordingly.
(function(l) {
if (l.search) {
var q = {};
l.search.slice(1).split('&').forEach(function(v) {
var a = v.split('=');
q[a[0]] = a.slice(1).join('=').replace(/~and~/g, '&');
});
if (q.p !== undefined) {
window.history.replaceState(null, null,
l.pathname.slice(0, -1) + (q.p || '') +
(q.q ? ('?' + q.q) : '') +
l.hash
);
}
}
}(window.location))</script>
<script src="static/js/main.js"></script>
<script src="static/js/interact.min.js"></script>
<script src="static/js/highlight.min.js"></script>
<script src="static/js/katex.min.js"></script>
<script src="static/js/html2canvas.min.js"></script>
<script src="static/js/code-editor.js"></script>
<script src="static/js/custom.js"></script>
</body>
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