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[[Binomialkoeffizient]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Flogseq____&quot;,74,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Vlogseq____&quot;,77,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,32,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;~:headinglogseq____&quot;,2],536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Hlogseq____&quot;,32,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-d376-410b-b426-00cc45a72dd9logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\frac12 \\\\sqrt2, \\\\frac12, \\\\frac12\\\\sqrt3 \\\\text{ sind werte von }\\\\sin x$\\n\\\\begin{align}\\n\\\\sin 30\\\\degreelogseq____&amp;=\\\\frac12\\\\\\\\\\n\\\\sin 45\\\\degree logseq____&amp;= \\\\frac12\\\\sqrt2 \\\\\\\\\\n\\\\sin 60\\\\degree logseq____&amp;= \\\\frac12 \\\\sqrt3 \\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Flogseq____&quot;,98,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Vlogseq____&quot;,98,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-d328-479b-a486-c349ffd70834logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\sqrt[n]{a^n}logseq____&amp;=1^\\\\frac nn=a^1=a\\\\\\\\\\n\\\\sqrt[n]{\\\\frac ab} logseq____&amp;= \\\\frac{\\\\sqrt[n]a}{\\\\sqrt[n]b}\\\\\\\\\\n\\\\left(\\\\sqrt[n]a\\\\right)^mlogseq____&amp;=a^\\\\frac mn\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Flogseq____&quot;,65,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Vlogseq____&quot;,59,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-b175-48ad-8eb0-ca7ad77720c9logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Potenzen]] und [[Wurzeln]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Flogseq____&quot;,85,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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x_1x_2=12=q\\\\\\\\\\nx^2+px+qlogseq____&amp;=0\\\\\\\\\\nx^2-7x+12logseq____&amp;=0\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Flogseq____&quot;,47,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Vlogseq____&quot;,47,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-fc6d-47fe-b38f-0c39decdd1belogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;https://www.wolframalpha.comlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Flogseq____&quot;,64,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Vlogseq____&quot;,64,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ulogseq____&quot;,44,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ulogseq____&quot;,46,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-9313-4461-9a01-7ff79879cfc7logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn }alogseq____&gt;0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=a\\\\sqrt{a}logseq____&amp;,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=a^2-\\\\sqrt{a}logseq____&amp;,f\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=\\\\sqrt{a^3}logseq____&amp;,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=a^{\\\\frac32}logseq____&amp;,r\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Flogseq____&quot;,67,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Vlogseq____&quot;,67,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-c260-4d73-98c3-56aa6c16fb6blogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]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;,99,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Vlogseq____&quot;,93,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[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;^Hlogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-5a99-497b-8e60-cd0c75e87378logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Für } x=\\\\frac25 \\\\text{ und } y=\\\\frac37 \\\\text{ ist }\\\\frac xy$\\n\\\\begin{align}\\n\\\\frac xy = \\\\frac{\\\\frac25}{\\\\frac37} = \\\\frac{2*7}{3*5}=\\\\frac{14}{15}\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Flogseq____&quot;,97,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Vlogseq____&quot;,97,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-34d2-4e0b-8fda-3e2971c38d74logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nax^2+bx+clogseq____&amp;=0logseq____&amp;|:a\\\\quadlogseq____&amp;a\\\\ne0\\\\\\\\\\nx^2+\\\\frac ba x + \\\\frac ca logseq____&amp;= 0\\\\\\\\\\nplogseq____&amp;=\\\\frac ba,logseq____&amp;q = \\\\frac ca\\\\\\\\\\nx^2+px+qlogseq____&amp;=0\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Flogseq____&quot;,66,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Vlogseq____&quot;,66,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-b7ec-465e-86eb-6344ee8b110elogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Wurzeln]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Flogseq____&quot;,93,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Vlogseq____&quot;,52,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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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;,[60,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Flogseq____&quot;,102,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Vlogseq____&quot;,85,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-5eb1-4760-8a27-68ac7914ade5logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Rationalmachen]] des [[Nenner]]slogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Flogseq____&quot;,68,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Vlogseq____&quot;,59,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Hlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Hlogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-6b5d-4541-9ca0-09aeffb35888logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Einsetzen, um zu überprüfen, ob man eine Fallunterscheidung brauchtlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Flogseq____&quot;,81,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Vlogseq____&quot;,91,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,30,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-bfed-4c05-a241-a89df03482dflogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[63,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;,[63,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Flogseq____&quot;,50,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Vlogseq____&quot;,98,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-b543-458b-bc9a-1a03745e964clogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wolframalpha]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Flogseq____&quot;,83,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Vlogseq____&quot;,83,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,44,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,46,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Hlogseq____&quot;,46,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-b14b-4b4f-bf4f-770746a06854logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Die Lösung von } x^n-a=0 \\\\text{ ist } x=\\\\sqrt[n]a$ #FIXME ich glaube hier fehlt logseq____&gt;0 constraintlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Flogseq____&quot;,59,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Vlogseq____&quot;,59,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Hlogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-4e73-4f4e-b562-862a7562a174logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Quadratische Gleichungen]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Flogseq____&quot;,59,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Vlogseq____&quot;,52,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Hlogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-5fab-4012-954c-611cc059a567logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Wurzeln]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Flogseq____&quot;,104,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Hlogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-5ad5-4aa6-bd57-8ca46901439flogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Allgemein}$\\n\\\\begin{align}\\n|y|logseq____&amp;=\\\\begin{cases}\\ny logseq____&amp;\\\\text{ falls } y\\\\ge0\\\\\\\\\\n-y logseq____&amp;\\\\text{ falls } ylogseq____&lt;0\\\\\\\\\\n\\\\end{cases}\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Flogseq____&quot;,96,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Vlogseq____&quot;,59,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[68,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-60c6-40ed-9135-4a253fda9b51logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[69,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;,[69,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Flogseq____&quot;,104,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Vlogseq____&quot;,104,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Ulogseq____&quot;,31,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-9794-46fb-8fee-613c01930e98logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Flogseq____&quot;,63,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Vlogseq____&quot;,63,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Hlogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-5d67-47aa-b4fb-e840c267989clogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Satz von Vieta]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&amp;=0 logseq____&amp;logseq____&amp; \\\\text{habe }x_{1,2}\\\\text{ als Lösung}\\\\\\\\\\nx_1+x_2logseq____&amp;=-p logseq____&amp;logseq____&amp; x_1*x_2=q\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Flogseq____&quot;,48,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Vlogseq____&quot;,92,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Hlogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-7d63-486c-899f-bc7a8e7317b5logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Allgemein}$\\n\\\\begin{align}\\n\\\\ln a + \\\\ln b logseq____&amp;= \\\\ln(a*b) \\\\\\\\\\n\\\\ln(-a) logseq____&amp;= \\\\frac1{\\\\ln 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[[Potenzen]]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;,83,536870919]],[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;,27,536870919]],[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;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-5b29-41da-8333-ee314039728flogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Binomische Formeln]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Flogseq____&quot;,98,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Hlogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-cab9-4c2a-9c5e-1f870ebcbce1logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Flogseq____&quot;,73,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Vlogseq____&quot;,74,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Hlogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-4e88-4af8-a8ca-25b792f922eclogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[87,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;,[87,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Flogseq____&quot;,56,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Vlogseq____&quot;,56,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-5ca6-4c72-a89b-5bd9eab6f9cdlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____&gt;0$ welche keinen Sinn ergibtlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Flogseq____&quot;,100,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Vlogseq____&quot;,96,536870919]],[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;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Hlogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-9ca3-47f9-875c-402c704f8ccelogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{array}{c}\\n{0\\\\choose 0}\\n\\\\\\\\\\n{1\\\\choose 0} {1\\\\choose 1}\\n\\\\\\\\\\n{2\\\\choose 0} {2\\\\choose 1} {2\\\\choose 2}\\n\\\\\\\\\\n{3\\\\choose 0} {3\\\\choose 1} {3\\\\choose 2} {3\\\\choose 3}\\n\\\\\\\\\\n\\\\cdots\\n\\\\end{array}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Flogseq____&quot;,90,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Vlogseq____&quot;,49,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,32,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-4bcd-4613-b6ec-2ef0b5393fbdlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____&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;,49,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Vlogseq____&quot;,49,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,32,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,38,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Hlogseq____&quot;,38,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-a78b-4195-bd4e-faa304ee1795logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Wurzelgleichung]]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;,66,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Vlogseq____&quot;,52,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,30,536870919]],[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;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Hlogseq____&quot;,30,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-22bb-4c0b-9738-11d7c23646c1logseq____&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;,58,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Vlogseq____&quot;,66,536870919]],[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;~u65294eea-b1f0-4374-8b5d-9a94c9e3e16clogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Potenzen]]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;,52,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Vlogseq____&quot;,52,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[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;^ 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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;,[121,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Flogseq____&quot;,117,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Xlogseq____&quot;,110,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Vlogseq____&quot;,117,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,108,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,109,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,110,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Hlogseq____&quot;,108,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Hlogseq____&quot;,109,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-f57c-449c-b323-fa34eb0088e7logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 2a}\\\\quad x\\\\ge-2$\\n\\\\begin{align}\\n|\\\\underbrace{x+2}_{\\\\ge0}logseq____&amp;=x+2\\\\\\\\\\n-x+3logseq____&amp;\\\\le x+2 logseq____&amp;|logseq____&amp; -2\\\\\\\\\\n-x+1logseq____&amp;\\\\le x logseq____&amp;|logseq____&amp; +x\\\\\\\\\\n\\\\frac12logseq____&amp;\\\\le x logseq____&amp;|logseq____&amp; :2\\\\\\\\\\n\\\\end{align}\\n\\\\begin{align}\\nL_2=\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|xlogseq____&lt;3,x\\\\ge-2,x\\\\ge\\\\frac12\\\\right\\\\}=\\\\left[\\\\frac12,3\\\\right)\\n\\\\end{align}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;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Xlogseq____&quot;,110,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Vlogseq____&quot;,129,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,106,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,109,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,110,536870920]],[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;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-91f1-4f00-ab31-704f6b90349elogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]\\n\\\\begin{align}\\n|5|=logseq____&amp;5\\\\\\\\\\n|-3,3|logseq____&amp;=3,3\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Flogseq____&quot;,121,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Xlogseq____&quot;,110,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Vlogseq____&quot;,117,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,109,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,110,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Hlogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-6350-4a0d-b878-a24edcea1024logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Menge 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;,[124,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Flogseq____&quot;,126,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Xlogseq____&quot;,110,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Vlogseq____&quot;,116,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,110,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-7e5a-4ce4-a969-d536ae30e3d3logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Menge aller reellen Zahlen zwischen 1 und 4 inklusive 1 und 4\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-1\\\\le x\\\\le4\\\\right\\\\}=:\\\\underbrace{[-1,4]}_\\\\text{Abgeschlossenes 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aller reellen Zahlen zwischen 1 und 4 ohne 1 und 4\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-1logseq____&lt;xlogseq____&lt;4\\\\right\\\\}=:\\\\underbrace{(-1,4)}_\\\\text{Offenes 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L_2=[3,\\\\infty)\\\\cup\\\\left[\\\\frac12,3\\\\right)=\\\\left[\\\\frac12,\\\\infty\\\\right)\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Flogseq____&quot;,130,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Xlogseq____&quot;,110,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Vlogseq____&quot;,129,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,106,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,109,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,110,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-ce35-4d9f-9941-4d86e382a054logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 1b}\\\\quad xlogseq____&lt;-2\\\\quad\\\\text{Wiederspricht Bedingung}\\\\quad x\\\\ge3$logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Flogseq____&quot;,133,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Xlogseq____&quot;,110,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Vlogseq____&quot;,129,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,106,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,109,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,110,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-a9f9-4ced-bdcf-b6fb9ef2a139logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Flogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Xlogseq____&quot;,110,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Vlogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,106,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,109,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,110,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Tantologie]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Flogseq____&quot;,183,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Xlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Vlogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Hlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-bc6f-4ab7-a504-0a310b2fcb12logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Verknüpfung von Aussagen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Flogseq____&quot;,161,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Xlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Vlogseq____&quot;,175,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Hlogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-e74b-4f69-83a4-b4b40776f277logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Flogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Xlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Vlogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Hlogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-cd5b-4278-93f8-376ef3ed42eclogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Variable]([[Variablen]]), die den Wert $w$ oder $f$ 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[[Kontradiktion]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Flogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Xlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Vlogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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$\\\\text{wahr}/\\\\text{falsch}$)logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Flogseq____&quot;,175,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Xlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Vlogseq____&quot;,175,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,145,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Hlogseq____&quot;,145,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-0b18-433d-8abc-1b3d0ea3d8a1logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Belegung]] (der 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[[Aussagenlogische Variable]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Flogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Xlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Vlogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Hlogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-22ca-4865-95c5-ba2dddfd64b7logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 1. [[Aussagen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Flogseq____&quot;,164,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Xlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Vlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Hlogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-999d-4e1c-9b22-464ea2ffdad3logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[176,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;,[176,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Flogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Xlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Vlogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Hlogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Hlogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Hlogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-739a-4f71-be70-a45b50726c6clogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[177,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;,[177,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Flogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Xlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Vlogseq____&quot;,183,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Hlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-8c0a-4843-a38d-b7c4e4a6067flogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $w$ istlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Flogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Xlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Vlogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-2a81-4cad-b9b1-1b0d78512d78logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[179,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;,[179,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Flogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Xlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Vlogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,151,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Hlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Hlogseq____&quot;,151,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Hlogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-a0eb-49b4-85e6-fc9ad0b139a5logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Flogseq____&quot;,183,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Xlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Vlogseq____&quot;,183,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,144,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,145,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Hlogseq____&quot;,144,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Hlogseq____&quot;,145,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Hlogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Hlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-2deb-4b95-9087-88ee4b4ffbeelogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Flogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Xlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Vlogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,42,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Ulogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Hlogseq____&quot;,42,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Hlogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-b33b-4a94-bd43-884014036fe3logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[182,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;,[182,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Flogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Xlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Vlogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Ulogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^Hlogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[182,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-7106-4941-bde1-6df515b4238dlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Flogseq____&quot;,172,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Xlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Vlogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ulogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Ulogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Hlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^Hlogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[183,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-645e-4185-be44-75ecaf8e7d84logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]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;,179,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Xlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Vlogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Ulogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^Hlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[184,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-c0c8-48d7-a8e5-524a4991d38blogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[185,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;,[185,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Flogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Xlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Vlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^Ulogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[185,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-6a83-4acf-85a9-afcebd08d1e1logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $f$ istlogseq____&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;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Xlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Vlogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,157,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eea-7075-4fcf-8964-2aa24dc3bcbelogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\np\\\\land q\\\\lor r\\\\\\\\\\n(p\\\\land q)\\\\lor r\\\\\\\\\\np\\\\land (q\\\\lor 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[[Regeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Flogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Vlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ulogseq____&quot;,189,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Allquantor]] 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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;,[219,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^Flogseq____&quot;,226,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^Vlogseq____&quot;,214,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-2572-4941-b320-08d839ba54f2logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[220,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativschreibweisen:\\n$\\\\forall 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q(u,w))\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Flogseq____&quot;,250,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Vlogseq____&quot;,250,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-fb69-48c5-85a5-d7c78ce1dddflogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x,y)$ AF in Variablen $x,y$ über $U_1,U_2$\\n\\\\begin{align}\\n\\\\underbrace{\\\\forall x: \\\\underbrace{\\\\exists y: p(x,y)}_{\\\\text{AF in den Variablen }x\\\\text{ über }U_1}}_{\\\\text{Aussage}}\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^Flogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^Vlogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^Ulogseq____&quot;,189,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-0476-412d-9b93-9a547f240913logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[223,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;,[223,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^Flogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^Vlogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^Ulogseq____&quot;,200,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^Ulogseq____&quot;,201,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-1f35-4920-8dca-39c03a3aa002logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[224,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXMElogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[224,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[224,logseq____&quot;^Flogseq____&quot;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[224,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[224,logseq____&quot;^Vlogseq____&quot;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[224,logseq____&quot;^Ulogseq____&quot;,42,536870923]],[logseq____&quot;^15logseq____&quot;,[224,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[224,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[224,logseq____&quot;^Hlogseq____&quot;,42,536870923]],[logseq____&quot;^15logseq____&quot;,[224,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[224,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-cb98-4aa4-bed6-d8c172cf10d5logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[225,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nlogseq____&amp;\\\\forall x: \\\\forall y: p(x, y) \\\\equiv \\\\forall y: \\\\forall x: p(x,y)\\\\\\\\\\nlogseq____&amp;\\\\exists x:\\\\exists y:p(x,y)\\\\equiv\\\\exists y:\\\\exists x:p(x,y)\\\\\\\\\\nlogseq____&amp;[\\\\forall x_1:\\\\forall x_2: \\\\cdots:\\\\forall x_n:p(x_1,x_2,\\\\cdots,x_n)\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\equiv\\\\forall_{x_{\\\\pi(1)}}:\\\\forall_{x_{\\\\pi(1)}}:\\\\cdots:\\\\forall_{x_{\\\\pi(1)}}:p(x_1,x_2,\\\\cdots,x_n)\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[225,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[225,logseq____&quot;^Flogseq____&quot;,238,536870923]],[logseq____&quot;^15logseq____&quot;,[225,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[225,logseq____&quot;^Vlogseq____&quot;,238,536870923]],[logseq____&quot;^15logseq____&quot;,[225,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[225,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[225,logseq____&quot;^Ulogseq____&quot;,201,536870923]],[logseq____&quot;^15logseq____&quot;,[225,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[225,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[225,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-a27f-45f4-b100-07f5d8bf3bbdlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[226,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Endliches Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[226,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[226,logseq____&quot;^Flogseq____&quot;,240,536870923]],[logseq____&quot;^15logseq____&quot;,[226,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[226,logseq____&quot;^Vlogseq____&quot;,214,536870923]],[logseq____&quot;^15logseq____&quot;,[226,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[226,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[226,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[226,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-6d76-48d8-91d7-f9c166e33211logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[227,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\blacksquare$ = Beweisende, auch [q.e.d.]([[Q.E.D.]]), [[w.z.b.w.]], QED, ![image.png](../assets/image_1697192491775_0.png)logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[227,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[227,logseq____&quot;^Flogseq____&quot;,244,536870923]],[logseq____&quot;^15logseq____&quot;,[227,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[227,logseq____&quot;^Vlogseq____&quot;,244,536870923]],[logseq____&quot;^15logseq____&quot;,[227,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[227,logseq____&quot;^Ulogseq____&quot;,191,536870923]],[logseq____&quot;^15logseq____&quot;,[227,logseq____&quot;^Ulogseq____&quot;,194,536870923]],[logseq____&quot;^15logseq____&quot;,[227,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[227,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[227,logseq____&quot;^Ulogseq____&quot;,200,536870923]],[logseq____&quot;^15logseq____&quot;,[227,logseq____&quot;^Ulogseq____&quot;,201,536870923]],[logseq____&quot;^15logseq____&quot;,[227,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[227,logseq____&quot;^Hlogseq____&quot;,191,536870923]],[logseq____&quot;^15logseq____&quot;,[227,logseq____&quot;^Hlogseq____&quot;,194,536870923]],[logseq____&quot;^15logseq____&quot;,[227,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[227,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-9347-466e-9741-d18175f28452logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[228,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:(p(x)\\\\land q(x)) logseq____&amp;\\\\equiv (\\\\forall x: p(x)) \\\\land (\\\\forall x:q(x));\\\\notag\\\\\\\\\\n\\\\exists x: (p(x) \\\\lor q(x)) logseq____&amp;\\\\equiv (\\\\exists x: p(x))\\\\lor(\\\\exists x: q(x)),\\\\quadlogseq____&amp;\\\\text{Große Assoziativgesetze}\\\\\\\\\\n\\\\neg(\\\\forall x:p(x))logseq____&amp;\\\\equiv \\\\exists x: (\\\\neg p(x));\\\\quadlogseq____&amp;\\\\text{Große de Morgansche Regeln;}\\\\notag\\\\\\\\\\n\\\\neg(\\\\exists x: p(x)) logseq____&amp;\\\\equiv \\\\forall x: (\\\\neg p(x)),\\\\quadlogseq____&amp;\\\\text{Negationsregeln.}\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[228,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[228,logseq____&quot;^Flogseq____&quot;,239,536870923]],[logseq____&quot;^15logseq____&quot;,[228,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[228,logseq____&quot;^Vlogseq____&quot;,239,536870923]],[logseq____&quot;^15logseq____&quot;,[228,logseq____&quot;^Ulogseq____&quot;,189,536870923]],[logseq____&quot;^15logseq____&quot;,[228,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[228,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[228,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[228,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-ed7c-434c-b1ce-99bae33ce909logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^Flogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^Vlogseq____&quot;,214,536870923]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^Hlogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-9392-4e05-ba8d-9f2a95c52bf8logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Aussageform]] (AF) über [Universen](Universen (Logik)) $U_1,\\\\cdots,U_n$:logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Flogseq____&quot;,214,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Vlogseq____&quot;,214,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Hlogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-a233-459d-b1e9-e1d846d5e04dlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[231,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;,[231,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^Flogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^Vlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-ce2d-44f2-9bc9-ae46384a7106logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Schachtelung von quantoren ([Beispiel]([[Beispiele]])):logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Flogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Vlogseq____&quot;,239,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Ulogseq____&quot;,189,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Hlogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-a11f-492b-83f4-c95574e49baelogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\exists x:p(x)$ ist die Aussage: \\logseq____&quot;Es gibt (wenigstens) ein x aus U für das $p(x)$ wahr ist\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w \\\\quadlogseq____&amp;\\\\text{falls }p(x)\\\\text{ w ist für (wenigstens) ein x aus U}\\\\\\\\f\\\\quad logseq____&amp;\\\\text{falls }p(x)\\\\text{ f ist für alle x aus U}\\\\end{cases}$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Flogseq____&quot;,219,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Vlogseq____&quot;,214,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Ulogseq____&quot;,145,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Hlogseq____&quot;,145,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-bde1-402c-8129-823edc697724logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist wahr}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Flogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Vlogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Ulogseq____&quot;,200,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Ulogseq____&quot;,201,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Hlogseq____&quot;,200,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-f171-4d4d-8ba9-125fe5f4d0e5logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[235,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;,[235,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Flogseq____&quot;,242,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Vlogseq____&quot;,242,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Ulogseq____&quot;,201,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-9179-4af6-8bc3-0755c7a1b01clogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Flogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Vlogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,189,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,192,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,204,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,209,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Hlogseq____&quot;,192,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Hlogseq____&quot;,204,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Hlogseq____&quot;,209,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-bd57-4fc3-9e79-4854e8b3a99flogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Die beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der [[Aussagenlogik]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Flogseq____&quot;,248,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Vlogseq____&quot;,214,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ulogseq____&quot;,193,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ulogseq____&quot;,211,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Hlogseq____&quot;,193,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Hlogseq____&quot;,211,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-5e65-43b8-8747-1b7c9e6ff360logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Gleichartige]([[Gleichartig]]) [[Quantoren]] dürfen vertauscht werdenlogseq____&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;,239,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Vlogseq____&quot;,214,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,201,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Hlogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Hlogseq____&quot;,201,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-f2a7-41df-9054-ce219f6f3a1blogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Regeln]]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;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Vlogseq____&quot;,214,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ulogseq____&quot;,189,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Hlogseq____&quot;,189,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-f36f-4117-a566-70576840a99elogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[240,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;,[240,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Flogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Vlogseq____&quot;,214,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-80c8-482c-8795-b05c2476ba2clogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\logseq____&quot;\\\\text{x ist prim}\\logseq____&quot; \\\\quad logseq____&amp; \\\\text{ist AF mit Variablen x über den natürlichen Zahlen}\\\\\\\\\\n\\logseq____&quot;\\\\underbrace{x}_{x_1}logseq____&lt;\\\\underbrace{y}_{x_2}\\logseq____&quot;\\\\quad logseq____&amp;\\\\text{ist AF mit Variablen }x,y\\\\text{ über die reellen Zahlen } \\\\underbrace{\\\\Reals}_{U_1},\\\\underbrace{\\\\Reals}_{U_2}\\\\\\\\\\n\\logseq____&quot;\\\\text{x ist wahr}\\logseq____&quot;\\\\quadlogseq____&amp;\\\\text{ist AF mit Variablen x über dem Universum der Aussagen}\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Flogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Vlogseq____&quot;,214,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-5553-4487-9ffb-880c49536502logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])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;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Vlogseq____&quot;,238,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,201,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Hlogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-7dce-4556-a87e-9f48010eedd3logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Nach Ersetzung von $x$ in der AF $\\logseq____&quot;xlogseq____&lt;y\\logseq____&quot;$ durch eine konkrete Zahl entsteht eine AF in der Variablen $y$, z. Bsp. $\\logseq____&quot;17logseq____&lt;y\\logseq____&quot;$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Flogseq____&quot;,241,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Vlogseq____&quot;,241,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-5fb2-4023-98cd-8c5af8f3de8flogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,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;,[244,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Flogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Xlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Vlogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,200,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,201,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65294eeb-02b6-4f85-b95f-ba0bcc97591blogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;wobei $\\\\pi$ eine \\logseq____&quot;[[Permutation]]\\logseq____&quot; der Zahl $(1,2,\\\\cdots,n)$ 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