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[[Pascalsches Dreieck]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Flogseq____&quot;,90,536870919]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Vlogseq____&quot;,76,536870919]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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ergibtlogseq____&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;,96,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Vlogseq____&quot;,55,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Hlogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-1f02-4236-977a-ec742cee7fd0logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wolframalpha]]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;,68,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Vlogseq____&quot;,68,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,44,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,46,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Hlogseq____&quot;,46,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-6f0b-4924-9f38-5cf932e5678elogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____&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;,72,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Vlogseq____&quot;,72,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,32,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,38,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Hlogseq____&quot;,38,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-052b-4b92-a7bb-370e64664825logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[52,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 a}\\\\\\\\\\n\\\\end{align}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;,61,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Vlogseq____&quot;,62,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,31,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-b251-4052-a60e-b28d6a077b91logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\sqrt{a+5}-\\\\sqrt{x+3}logseq____&amp;=2\\\\sqrt(x+1) logseq____&amp;|logseq____&amp;()^2\\\\\\\\\\n\\\\left(\\\\sqrt{x+5}-\\\\sqrt{x+3}\\\\right)^2logseq____&amp;=4(x+1)\\\\\\\\\\n(x+5)-2\\\\sqrt{x+5}\\\\sqrt{x+3}+(x+3)logseq____&amp;=4x+4logseq____&amp;|logseq____&amp;-(2x+8)\\\\\\\\\\n-2\\\\sqrt{(x+5)(x+3)}logseq____&amp;=2x-4 logseq____&amp;|logseq____&amp;()^2\\\\\\\\\\n4(x+5)(x+3)logseq____&amp;=4x^2-16x+16\\\\\\\\\\n4x^2+32x+60logseq____&amp;=4x^2-16x+16logseq____&amp;|logseq____&amp;-4x^2+16x-16\\\\\\\\\\n48x+44logseq____&amp;=0\\\\quad x=-\\\\frac{11}{12}\\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;,93,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Vlogseq____&quot;,93,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,30,536870919]],[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;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-bb23-445c-9d09-1c320ee6f0c4logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[54,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;,[54,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Flogseq____&quot;,89,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Vlogseq____&quot;,89,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-1094-4ffe-83dc-2ed4c1ba0894logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]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;,102,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Vlogseq____&quot;,63,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[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;^Hlogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-e4c4-4928-adf8-53faae069125logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Was ist Größer?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;,89,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-dff7-430a-a62c-5cbb2d349097logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]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;,59,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Vlogseq____&quot;,71,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Hlogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-44aa-4d1c-8405-e4cefdff3495logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])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;,103,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Vlogseq____&quot;,103,536870919]],[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;,35,536870919]],[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;^Ulogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Hlogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-5735-4f04-99a4-46374d4bfa6clogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Wenn }alogseq____&gt;0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac b{\\\\sqrt a} = \\\\frac b{\\\\sqrt a}*\\\\frac{\\\\sqrt a}{\\\\sqrt a} = \\\\frac {b\\\\sqrt a}a\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Flogseq____&quot;,71,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Vlogseq____&quot;,71,536870919]],[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;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-65cb-4e27-a749-2226967bb75dlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[60,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;,[60,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Flogseq____&quot;,66,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Vlogseq____&quot;,80,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Hlogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-3297-4513-b36a-03a12f1a49adlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche 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[[Binomialkoeffizient]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Flogseq____&quot;,80,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Vlogseq____&quot;,48,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,32,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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ca\\\\\\\\\\nx^2+px+qlogseq____&amp;=0\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Flogseq____&quot;,95,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Vlogseq____&quot;,95,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-69d4-4d7f-84e3-ffcf0ae4079flogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\underbrace{\\\\frac6{2+\\\\sqrt2}*\\\\frac{2-\\\\sqrt2}{2-\\\\sqrt2}\\n= \\\\frac{6(2-\\\\sqrt2)}{2^2-(\\\\sqrt2)^2}}_\\\\text{3. binomische Formel}\\nlogseq____&amp;=\\\\frac{6(2-\\\\sqrt2)}2=3(2-\\\\sqrt2)\\\\\\\\\\n\\\\frac{a-b}{\\\\sqrt a+\\\\sqrt b}logseq____&amp;=\\\\frac{a-b}{\\\\sqrt a + \\\\sqrt b}\\\\frac{\\\\sqrt a-\\\\sqrt b}{\\\\sqrt a-\\\\sqrt b}logseq____&amp;, a,b,logseq____&gt;0\\\\notag\\\\\\\\\\n=\\\\frac{(a-b)(\\\\sqrt a-\\\\sqrt b)}{(a-b)}logseq____&amp;=\\\\sqrt a\\\\sqrt b\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Flogseq____&quot;,57,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Vlogseq____&quot;,57,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,45,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-15de-4bc5-9c56-119183c59c4dlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[75,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;,[75,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Flogseq____&quot;,87,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Vlogseq____&quot;,88,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-e12d-44b9-b1e7-d336d18312f2logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Binomische Formeln]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Flogseq____&quot;,88,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Hlogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-1dc7-4f5f-ab04-c88f6afecc65logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Allgemein}$\\n\\\\begin{align}\\n(a+b)^2logseq____&amp;=a^2+2ab+b^2logseq____&amp;,\\\\text{ 1. Binomische Formel}\\\\\\\\\\n(a-b)^2logseq____&amp;=a^2-2ab+b^2logseq____&amp;,\\\\text{ 2. Binomische Formel}\\\\\\\\\\n(a+b)(a-b)logseq____&amp;=a^2-b^2logseq____&amp;,\\\\text{ 3. Binomische Formel}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Flogseq____&quot;,76,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Vlogseq____&quot;,76,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-51e9-4da1-be60-cd41b195d745logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Flogseq____&quot;,75,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Vlogseq____&quot;,75,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Hlogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-bdde-4020-b478-8a28ac52ca27logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[79,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;,[79,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Flogseq____&quot;,63,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Vlogseq____&quot;,63,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Hlogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-f290-4cb9-ad2c-8e38a3eb8047logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Flogseq____&quot;,94,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Vlogseq____&quot;,48,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Hlogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-f6e5-4f11-8828-4443c36e73f1logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;cosa -logseq____&gt; beliebige Variable\\ncubus -logseq____&gt; hoch 3logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Flogseq____&quot;,70,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Vlogseq____&quot;,70,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-d100-4a29-95c8-1291bfd7c18clogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Herleitung mit }$[[Quadratische Ergänzung]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&amp;=0logseq____&amp;|logseq____&amp;-q\\\\\\\\\\nx^2+pxlogseq____&amp;=-qlogseq____&amp;|logseq____&amp;+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\nx^2+px+\\\\left(\\\\frac p2\\\\right)^2logseq____&amp;=-q+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\n\\\\underbrace{\\\\left(x+\\\\frac p2\\\\right)^2}_\\\\text{1. binomische Formel}logseq____&amp;=-q+\\\\left(\\\\frac p2\\\\right)^2logseq____&amp;|logseq____&amp;\\\\sqrt{()}\\\\\\\\\\n\\\\left|x+\\\\frac p2\\\\right|logseq____&amp;=\\\\sqrt{\\\\frac{p^2}4-q}logseq____&amp;,logseq____&amp;\\\\text{ falls }\\\\frac{p^2}4-q\\\\ge0\\\\\\\\\\nx+\\\\frac p2logseq____&amp;=\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}logseq____&amp;|logseq____&amp;-\\\\frac p2\\\\\\\\\\nxlogseq____&amp;=-\\\\frac p2\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Flogseq____&quot;,85,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Vlogseq____&quot;,85,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,26,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Hlogseq____&quot;,26,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-70f6-4095-84d8-d5e156b0c512logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Häufige Falle:}$\\n\\\\begin{align}\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&amp;=(-1)^\\\\frac22logseq____&amp;=(-1)^1logseq____&amp;=-1\\\\\\\\\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&amp;=1^\\\\frac12logseq____&amp;logseq____&amp;=1\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Flogseq____&quot;,54,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Vlogseq____&quot;,89,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-a1f0-477f-8c83-9e73721f5ad3logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[84,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;,[84,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Flogseq____&quot;,56,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Vlogseq____&quot;,56,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-e83d-4ac1-9203-d11f2d6e2d32logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[pq-Formel]]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;,73,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Vlogseq____&quot;,95,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,43,536870919]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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\\\\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;,[87,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Flogseq____&quot;,88,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Vlogseq____&quot;,88,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[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;~u65297c63-a1a1-49b0-b41b-e4f804d59a09logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Trigonometrie]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Flogseq____&quot;,56,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Wurzeln]]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;,62,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Vlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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15 logseq____&amp;logseq____&amp; 6 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^7logseq____&amp;1 logseq____&amp;logseq____&amp; 7 logseq____&amp;logseq____&amp;21 logseq____&amp;logseq____&amp; 35 logseq____&amp;logseq____&amp; 35 logseq____&amp;logseq____&amp; 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[[Quadratische Gleichungen]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Flogseq____&quot;,63,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Vlogseq____&quot;,92,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Potenzen]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Flogseq____&quot;,92,536870919]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Xlogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Vlogseq____&quot;,92,536870919]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Ulogseq____&quot;,37,536870919]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Ulogseq____&quot;,40,536870919]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870920]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Jlogseq____&quot;,[],536870920]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Hlogseq____&quot;,109,536870920]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-0c69-494e-8a18-2c007fbf0518logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Betrag]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Flogseq____&quot;,117,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Vlogseq____&quot;,125,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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2b}\\\\quad xlogseq____&lt;-2$\\n\\\\begin{align}\\n|\\\\underbrace{x+2}_{logseq____&lt;0}logseq____&amp;=-(x+2)=-x-2\\\\\\\\\\n-x+3logseq____&amp;\\\\le -x-2 logseq____&amp;|logseq____&amp;+x\\\\\\\\\\n3logseq____&amp;\\\\le-2logseq____&amp;logseq____&amp;\\\\underset{falsche 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bei [[Ungleichungen]] sind Anwendbar aberlogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^Flogseq____&quot;,116,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^Vlogseq____&quot;,116,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^Ulogseq____&quot;,108,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^Ulogseq____&quot;,111,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^Ulogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^Hlogseq____&quot;,108,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[138,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-273d-4794-9486-a4a9a4b63da3logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Menge aller reellen Zahlen zwischen 1 und 4 inklusive 1 und 4\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-1\\\\le x\\\\le4\\\\right\\\\}=:\\\\underbrace{[-1,4]}_\\\\text{Abgeschlossenes Interval}\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Flogseq____&quot;,117,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Xlogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Vlogseq____&quot;,117,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Ulogseq____&quot;,35,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Ulogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Ulogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c63-2038-4933-b100-cb5384115a33logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[140,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; 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Lösung mit 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Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Nietzsche ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Flogseq____&quot;,205,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Vlogseq____&quot;,189,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[186,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-4165-450c-b9f5-977e0a8003a4logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussagenlogische Variable]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Flogseq____&quot;,208,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Vlogseq____&quot;,206,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,163,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^Hlogseq____&quot;,163,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[187,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-fe77-4e68-a2dd-2f8a45cca087logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Belegung]] (der [[Variablen]])logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Flogseq____&quot;,195,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Vlogseq____&quot;,206,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Hlogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^Hlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[188,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-306e-438c-9daa-0f1b3ce6d411logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 1. [[Aussagen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Flogseq____&quot;,201,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Vlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Hlogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-34a6-4e7b-9958-8c09821fdd87logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Weitere [[Beispiele]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Flogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Vlogseq____&quot;,206,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^Hlogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[190,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-5591-4f4c-a71a-f2733a215883logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[191,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;,[191,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Flogseq____&quot;,203,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Vlogseq____&quot;,192,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^Hlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[191,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-3143-43d0-a267-20a431c64c3dlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Flogseq____&quot;,188,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Vlogseq____&quot;,206,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Hlogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^Hlogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[192,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-c943-46ac-9094-e1add32a3c0dlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $f$ istlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Flogseq____&quot;,198,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Vlogseq____&quot;,198,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,169,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[193,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-f752-49f9-8549-52ab875552c8logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[194,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formeln $p,q$ [[logisch äquivalent]], wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv 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[[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Flogseq____&quot;,187,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Vlogseq____&quot;,206,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^Hlogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[195,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-9f61-4e43-b64e-fd4c49b3bfa5logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Flogseq____&quot;,197,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Vlogseq____&quot;,206,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^Hlogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[196,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-bc77-4a07-af3d-58fe2f9315c0logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[197,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;,[197,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Flogseq____&quot;,206,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Vlogseq____&quot;,206,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^Hlogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[197,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-e6ee-4c66-b41d-79ab5d35f6bclogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Kontradiktion]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Flogseq____&quot;,181,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Vlogseq____&quot;,206,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,169,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^Hlogseq____&quot;,169,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[198,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-cb1d-497f-92f4-279f8a86c945logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;C. Meinel, M. Mundhenk, [[\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. Auflage 2011]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Flogseq____&quot;,201,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Vlogseq____&quot;,201,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Ulogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^Hlogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[199,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-f220-4307-b28d-ef3df435cefalogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[200,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;,[200,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Flogseq____&quot;,190,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Vlogseq____&quot;,190,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[200,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-fb6f-4ad7-b898-e64ef886e665logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Büchertiplogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Flogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Vlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^17logseq____&quot;,false,536870922]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-c0ad-45ed-9842-39f667402954logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\np\\\\land q\\\\lor r\\\\\\\\\\n(p\\\\land q)\\\\lor r\\\\\\\\\\np\\\\land (q\\\\lor r)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Flogseq____&quot;,196,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Vlogseq____&quot;,196,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,35,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-23b1-489f-82c9-955fa6c1ea03logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Flogseq____&quot;,192,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Vlogseq____&quot;,192,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,162,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Hlogseq____&quot;,165,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Hlogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Hlogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Hlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-bc85-4896-a7c9-4138933cf5dblogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $w$ istlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Flogseq____&quot;,181,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Vlogseq____&quot;,181,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-028a-4974-9dd5-831d73802b21logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Satz, der wahr oder falsch ist, d.h. der [[Wahrheitswert]] $w$ bzw $f$ hat ($t/f$, $1/0$, $\\\\text{wahr}/\\\\text{falsch}$)logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Flogseq____&quot;,189,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Vlogseq____&quot;,189,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Hlogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-30a7-4f29-9b90-9cfbc9f4be09logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Verknüpfung von Aussagen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Flogseq____&quot;,186,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Vlogseq____&quot;,189,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Hlogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-3bcd-4570-8824-bdc168f96b1alogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Flogseq____&quot;,195,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Vlogseq____&quot;,195,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ulogseq____&quot;,42,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ulogseq____&quot;,175,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ulogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Hlogseq____&quot;,42,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Hlogseq____&quot;,175,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-c766-4fd3-a253-888d199c4036logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[208,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;,[208,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Flogseq____&quot;,196,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Xlogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Vlogseq____&quot;,206,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,171,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,177,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Hlogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Hlogseq____&quot;,171,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Hlogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Hlogseq____&quot;,177,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-0992-40a2-b8c2-768a1c77183clogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Klogseq____&quot;,1697217636418,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;regelnlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^11logseq____&quot;,logseq____&quot;Regelnlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Blogseq____&quot;,1697217636418,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-e19b-4074-8c3f-cc8c61415230logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Klogseq____&quot;,1697217636399,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;de morgansche regelnlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^11logseq____&quot;,logseq____&quot;de Morgansche Regelnlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Blogseq____&quot;,1697217636399,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-2b5e-4ddf-88ed-2c94f9144bbdlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Klogseq____&quot;,1697217636428,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;q.e.d.logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^11logseq____&quot;,logseq____&quot;Q.E.D.logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Blogseq____&quot;,1697217636428,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-09fc-416f-8978-e9f031460969logseq____&quot;,536870931]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Klogseq____&quot;,1697217636421,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;große de morgansche regelnlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^11logseq____&quot;,logseq____&quot;Große de Morgansche Regelnlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Blogseq____&quot;,1697217636421,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-e8e0-436c-b5fd-51fbbf3b544blogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Klogseq____&quot;,1697217636415,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;aussagenlogiklogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^11logseq____&quot;,logseq____&quot;Aussagenlogiklogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Blogseq____&quot;,1697217636415,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-713e-4215-b431-43e2b613fa99logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Klogseq____&quot;,1697217636427,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;w.z.b.w.logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^11logseq____&quot;,logseq____&quot;w.z.b.w.logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Blogseq____&quot;,1697217636427,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-d245-4b23-be9b-ed571456b7c0logseq____&quot;,536870931]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Klogseq____&quot;,1697217636402,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;kommutativlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^11logseq____&quot;,logseq____&quot;kommutativlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Blogseq____&quot;,1697217636402,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-294b-4dcf-9d2c-5a9e5551c1d7logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Klogseq____&quot;,1697217636426,536870923]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;grundlagen 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$\\\\pi$ eine \\logseq____&quot;[[Permutation]]\\logseq____&quot; der Zahl $(1,2,\\\\cdots,n)$ 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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;,[246,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Flogseq____&quot;,264,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-890b-4c21-b3ad-b070a6504f31logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Regeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Flogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Vlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Hlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^17logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-251f-4379-a463-428fa5dc772flogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[248,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;,[248,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Flogseq____&quot;,259,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Vlogseq____&quot;,259,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-0370-4575-8136-3db2025f58calogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[249,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;,[249,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Flogseq____&quot;,268,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Vlogseq____&quot;,268,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-4a62-4885-be13-44fee4d90e7dlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[250,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 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mit [[Variablen]] $x_1,\\\\cdots,x_n$, der bei Ersetzung jedes $x_j$ durch ein [Objekt]([[Objekt (Logik)]]) aus $U_j$ stets zu einer [Aussage]([[Aussagen]]) wirdlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Flogseq____&quot;,257,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,170,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,174,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,231,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Hlogseq____&quot;,170,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Hlogseq____&quot;,174,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Hlogseq____&quot;,231,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Hlogseq____&quot;,234,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-ae73-4a41-bdc8-9d5b97152cadlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist 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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;,[254,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Flogseq____&quot;,272,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-c16a-4299-b8ce-faaeb6261aa1logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[255,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;,[255,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Flogseq____&quot;,238,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-b88f-4dd7-b61b-b416f3409272logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Allquantor]] [[Existenzquantor]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Flogseq____&quot;,254,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Vlogseq____&quot;,254,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Hlogseq____&quot;,223,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Hlogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-19d4-4a9b-971f-cb61d2b361f8logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Aussageform]] (AF) über [Universen]([[Universen (Logik)]]) $U_1,\\\\cdots,U_n$:logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Flogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Hlogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Hlogseq____&quot;,232,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-6ff8-47af-b5d2-64b7fde36dcblogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[258,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;,[258,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Flogseq____&quot;,267,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Vlogseq____&quot;,267,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,212,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,215,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Hlogseq____&quot;,212,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Hlogseq____&quot;,215,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-ef49-4a0e-af8c-1782627bf026logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Flogseq____&quot;,260,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Vlogseq____&quot;,261,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Hlogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-f990-4b6f-9c30-ed69d5debb2elogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[260,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;,[260,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Flogseq____&quot;,261,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Vlogseq____&quot;,261,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-4728-4407-b274-b01b661c8886logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Gleichartige]([[Gleichartig]]) [[Quantoren]] dürfen vertauscht werdenlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Flogseq____&quot;,268,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Hlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Hlogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-4d6c-4aad-8750-150e3f1f1ba0logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[262,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;,[262,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Flogseq____&quot;,247,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Vlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-7563-4776-9f59-90c2b9d705b9logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativschreibweisen:\\n$\\\\forall x: p(x)$ auch $\\\\bigwedge x:p(x)$\\n$\\\\exists x:p(x)$ auch $\\\\bigvee x:p(x)$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Flogseq____&quot;,266,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-36a3-49cb-837e-d6d79d1f3b2blogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Die beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der [[Aussagenlogik]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Flogseq____&quot;,273,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,214,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Hlogseq____&quot;,214,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Hlogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-8dd2-4790-aade-ed48e90a4ed3logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Aussageform]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Flogseq____&quot;,262,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Vlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Hlogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-7730-433a-8cb2-04396c53d34flogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[266,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;,[266,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Flogseq____&quot;,254,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,166,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Hlogseq____&quot;,166,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-89c2-4ff1-84ae-1b22a7866e9blogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[267,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;,[267,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Flogseq____&quot;,252,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Vlogseq____&quot;,252,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-e6b4-4ca5-98e1-e8bb58ddd3dflogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Regeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Flogseq____&quot;,263,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^Hlogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[268,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-61f1-4e41-a731-719243ade4b4logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Flogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Vlogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Ulogseq____&quot;,230,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Hlogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Hlogseq____&quot;,225,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^Hlogseq____&quot;,230,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[269,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-d1b7-479d-9d33-ed4469016339logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Schachtelung von quantoren ([Beispiel]([[Beispiele]])):logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Flogseq____&quot;,249,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Vlogseq____&quot;,268,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,210,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^Hlogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[270,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-4c7d-4a15-95fd-bacd4b8bd3a8logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[271,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;,[271,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Flogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Vlogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,35,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,222,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[271,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-2c15-48d5-9ebd-da511ca1e7c0logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Endliches Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Flogseq____&quot;,246,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[272,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-64c4-4cde-81d0-254893b34194logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x)$ AF in der Variablen $x$ über $U$:logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Flogseq____&quot;,255,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Xlogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Vlogseq____&quot;,265,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Ulogseq____&quot;,217,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^Ulogseq____&quot;,228,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[273,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-ce75-4ab5-8593-1f4e13ec95b3logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[275,logseq____&quot;^Klogseq____&quot;,1697217636519,536870924]],[logseq____&quot;^15logseq____&quot;,[275,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[275,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;logarithmusgesetzelogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[275,logseq____&quot;^11logseq____&quot;,logseq____&quot;Logarithmusgesetzelogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[275,logseq____&quot;^Blogseq____&quot;,1697217636519,536870924]],[logseq____&quot;^15logseq____&quot;,[275,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-58f1-4310-b340-c0f77230a78clogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Logarithmusgesetze]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^Flogseq____&quot;,31,536870924]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^Xlogseq____&quot;,31,536870924]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^Vlogseq____&quot;,31,536870924]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^Ulogseq____&quot;,31,536870924]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^Ulogseq____&quot;,275,536870924]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^Hlogseq____&quot;,275,536870924]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[276,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-31bd-4bb2-872c-2d4fcbc2366flogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[277,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[277,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[277,logseq____&quot;^Flogseq____&quot;,276,536870924]],[logseq____&quot;^15logseq____&quot;,[277,logseq____&quot;^Xlogseq____&quot;,31,536870924]],[logseq____&quot;^15logseq____&quot;,[277,logseq____&quot;^Vlogseq____&quot;,31,536870924]],[logseq____&quot;^15logseq____&quot;,[277,logseq____&quot;^Ulogseq____&quot;,31,536870924]],[logseq____&quot;^15logseq____&quot;,[277,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[277,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-156c-453e-b582-c77727c9a6eflogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[290,logseq____&quot;^Klogseq____&quot;,1697217636566,536870927]],[logseq____&quot;^15logseq____&quot;,[290,logseq____&quot;^@logseq____&quot;,false,536870927]],[logseq____&quot;^15logseq____&quot;,[290,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;programmierung und algorithmenlogseq____&quot;,536870927]],[logseq____&quot;^15logseq____&quot;,[290,logseq____&quot;^11logseq____&quot;,logseq____&quot;Programmierung und Algorithmenlogseq____&quot;,536870927]],[logseq____&quot;^15logseq____&quot;,[290,logseq____&quot;^Blogseq____&quot;,1697217636566,536870927]],[logseq____&quot;^15logseq____&quot;,[290,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-c1cf-4384-a7a7-2bbccd228408logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[291,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Informationenlogseq____&quot;,536870927]],[logseq____&quot;^15logseq____&quot;,[291,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870927]],[logseq____&quot;^15logseq____&quot;,[291,logseq____&quot;^Flogseq____&quot;,290,536870927]],[logseq____&quot;^15logseq____&quot;,[291,logseq____&quot;^Xlogseq____&quot;,290,536870927]],[logseq____&quot;^15logseq____&quot;,[291,logseq____&quot;^Vlogseq____&quot;,290,536870927]],[logseq____&quot;^15logseq____&quot;,[291,logseq____&quot;^Ulogseq____&quot;,290,536870927]],[logseq____&quot;^15logseq____&quot;,[291,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870927]],[logseq____&quot;^15logseq____&quot;,[291,logseq____&quot;^Jlogseq____&quot;,[],536870927]],[logseq____&quot;^15logseq____&quot;,[291,logseq____&quot;^17logseq____&quot;,false,536870927]],[logseq____&quot;^15logseq____&quot;,[291,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-b19a-413b-ad3a-cce9c89f7385logseq____&quot;,536870927]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Bestehquote: 40%logseq____&quot;,536870927]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870927]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Flogseq____&quot;,291,536870927]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Xlogseq____&quot;,290,536870927]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Vlogseq____&quot;,291,536870927]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Ulogseq____&quot;,290,536870927]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^17logseq____&quot;,true,536870927]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-fa24-431d-92ec-5c52b480ef17logseq____&quot;,536870927]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## Bonuspunktelogseq____&quot;,536870927]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870927]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Flogseq____&quot;,292,536870927]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Xlogseq____&quot;,290,536870927]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Vlogseq____&quot;,291,536870927]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Ulogseq____&quot;,290,536870927]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870927]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Jlogseq____&quot;,[],536870927]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^17logseq____&quot;,true,536870927]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-20c8-4ec7-a140-5308062655c7logseq____&quot;,536870927]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Übungsblätter abgebenlogseq____&quot;,536870927]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870927]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Flogseq____&quot;,293,536870927]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Xlogseq____&quot;,290,536870927]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Vlogseq____&quot;,293,536870927]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Ulogseq____&quot;,290,536870927]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^17logseq____&quot;,true,536870927]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-50aa-4d9e-afe4-6145ec0be592logseq____&quot;,536870927]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Übungsprüfungenlogseq____&quot;,536870927]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870927]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Flogseq____&quot;,294,536870927]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Xlogseq____&quot;,290,536870927]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Vlogseq____&quot;,293,536870927]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Ulogseq____&quot;,290,536870927]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^17logseq____&quot;,true,536870927]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-b932-4eae-9264-4d09c371b8b9logseq____&quot;,536870927]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Bedeutunglogseq____&quot;,536870928]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870928]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Flogseq____&quot;,212,536870928]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Xlogseq____&quot;,212,536870928]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Vlogseq____&quot;,212,536870928]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Ulogseq____&quot;,212,536870928]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870928]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Jlogseq____&quot;,[],536870928]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^17logseq____&quot;,false,536870928]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-9e4c-434e-bae5-25324074f8d8logseq____&quot;,536870928]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Q.E.D. = \\logseq____&quot;quod erat demonstrandum\\logseq____&quot;logseq____&quot;,536870928]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870928]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Flogseq____&quot;,297,536870928]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Xlogseq____&quot;,212,536870928]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Vlogseq____&quot;,297,536870928]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Ulogseq____&quot;,212,536870928]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^17logseq____&quot;,true,536870928]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-7496-40b4-9d87-e93701fa71f6logseq____&quot;,536870928]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;lat. für \\logseq____&quot;was zu beweisen wahr\\logseq____&quot; (siehe [[w.z.b.w.]])logseq____&quot;,536870928]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870928]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Flogseq____&quot;,298,536870928]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Xlogseq____&quot;,212,536870928]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Vlogseq____&quot;,297,536870928]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Ulogseq____&quot;,212,536870928]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Ulogseq____&quot;,215,536870928]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Hlogseq____&quot;,215,536870928]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^17logseq____&quot;,true,536870928]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-083a-4fe3-a6f8-689e9ed9464alogseq____&quot;,536870928]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Signalisiert das Ende eines Beweiseslogseq____&quot;,536870928]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870928]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Flogseq____&quot;,299,536870928]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Xlogseq____&quot;,212,536870928]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Vlogseq____&quot;,297,536870928]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,212,536870928]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^17logseq____&quot;,true,536870928]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-89a4-44a2-9eec-db393bf4b72alogseq____&quot;,536870928]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Klogseq____&quot;,1697217636606,536870929]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^@logseq____&quot;,false,536870929]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;ungleichheitszeichenlogseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^11logseq____&quot;,logseq____&quot;Ungleichheitszeichenlogseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Blogseq____&quot;,1697217636606,536870929]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-6519-4f77-937d-80f88170c1c4logseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Klogseq____&quot;,1697217636607,536870929]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^@logseq____&quot;,false,536870929]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;divisionlogseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^11logseq____&quot;,logseq____&quot;Divisionlogseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Blogseq____&quot;,1697217636607,536870929]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-4c4e-4022-a14a-41e1e361773clogseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Klogseq____&quot;,1697217636608,536870929]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^@logseq____&quot;,false,536870929]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;multiplikationlogseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^11logseq____&quot;,logseq____&quot;Multiplikationlogseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Blogseq____&quot;,1697217636608,536870929]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-2e1a-4f2c-aeac-79395b04ccd9logseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Regelnlogseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Flogseq____&quot;,108,536870929]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Xlogseq____&quot;,108,536870929]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Vlogseq____&quot;,108,536870929]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,108,536870929]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870929]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Jlogseq____&quot;,[],536870929]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^17logseq____&quot;,false,536870929]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-e4ab-400a-a412-c335f33fa804logseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Bei [[Multiplikation]] oder [[Division]] mit einer negativen Zahl wird das [[Ungleichheitszeichen]] umgekehrtlogseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Flogseq____&quot;,305,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Xlogseq____&quot;,108,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Vlogseq____&quot;,305,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,108,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,302,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,303,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,304,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Hlogseq____&quot;,302,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Hlogseq____&quot;,303,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Hlogseq____&quot;,304,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^17logseq____&quot;,true,536870929]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-0d32-46a9-9de4-43003bb7710dlogseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\logseq____&quot;logseq____&gt;\\logseq____&quot;logseq____&amp;\\\\rightarrow\\logseq____&quot;logseq____&lt;\\logseq____&quot;\\\\\\\\\\n\\logseq____&quot;logseq____&lt;\\logseq____&quot;logseq____&amp;\\\\rightarrow\\logseq____&quot;logseq____&gt;\\logseq____&quot;\\\\\\\\\\n\\logseq____&quot;\\\\ge\\logseq____&quot;logseq____&amp;\\\\rightarrow\\logseq____&quot;\\\\le\\logseq____&quot;\\\\\\\\\\n\\logseq____&quot;\\\\le\\logseq____&quot;logseq____&amp;\\\\rightarrow\\logseq____&quot;\\\\ge\\logseq____&quot;\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Flogseq____&quot;,306,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Xlogseq____&quot;,108,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Vlogseq____&quot;,306,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,108,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,302,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,303,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,304,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^17logseq____&quot;,true,536870929]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-b0c0-4405-9765-d79330c6564alogseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;logseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Flogseq____&quot;,307,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Xlogseq____&quot;,108,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Vlogseq____&quot;,306,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,108,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,302,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,303,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,304,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^17logseq____&quot;,true,536870929]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-f2c3-47bb-b674-81818b4c73felogseq____&quot;,536870929]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Klogseq____&quot;,1697217636644,536870930]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^@logseq____&quot;,false,536870930]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;vorlesungs notizenlogseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^11logseq____&quot;,logseq____&quot;Vorlesungs Notizenlogseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Blogseq____&quot;,1697217636644,536870930]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-ebff-48a4-9fb5-8abc983aeabclogseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;each \\logseq____&quot;.excalidraw\\logseq____&quot; drawing file should have an equivalent \\logseq____&quot;.svg\\logseq____&quot; file in logseq____&lt;vault pathlogseq____&gt;/assets/excalidraw_svg with the same basenamelogseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Flogseq____&quot;,319,536870930]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Xlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Vlogseq____&quot;,317,536870930]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^17logseq____&quot;,true,536870930]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-3c31-4d02-b91f-cfbc14d87a92logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Click \\logseq____&quot;SVG\\logseq____&quot; and copy to logseq____&lt;vault pathlogseq____&gt;/assets/excalidraw_svgslogseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Flogseq____&quot;,315,536870930]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Xlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Vlogseq____&quot;,318,536870930]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^17logseq____&quot;,true,536870930]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-050c-458e-9d0e-ea511f66a5a9logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### Example\\n```\\nlogseq____&lt;vault pathlogseq____&gt;/draws/2023-10-08-21-23-31.excalidraw\\nlogseq____&lt;vault pathlogseq____&gt;/assets/excalidraw_svg/2023-10-08-21-23-31.svg\\n```logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Flogseq____&quot;,311,536870930]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Xlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Vlogseq____&quot;,317,536870930]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870930]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Jlogseq____&quot;,[],536870930]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^17logseq____&quot;,true,536870930]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-768f-4e5c-bd32-376126e8ad92logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;logseq____&lt;h1 style=\\logseq____&quot;color: red;\\logseq____&quot;logseq____&gt;Some drawings were not loadedlogseq____&lt;/h1logseq____&gt;logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Flogseq____&quot;,322,536870930]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Xlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Vlogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,310,536870930]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^17logseq____&quot;,true,536870930]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65297c64-13cc-4515-984f-06e567620afalogseq____&quot;,536870930]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Enable \\logseq____&quot;Background\\logseq____&quot; and check if you need Dark or Light 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