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constraintlogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Flogseq____&quot;,62,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Vlogseq____&quot;,62,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Ulogseq____&quot;,38,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Hlogseq____&quot;,38,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-af77-4b7a-8554-984f5229a564logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wolframalpha]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Flogseq____&quot;,76,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Vlogseq____&quot;,76,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Ulogseq____&quot;,40,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Ulogseq____&quot;,42,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Hlogseq____&quot;,42,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-1880-484c-9c27-95348d30f17blogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\n\\\\sqrt{x^4+6x^2y+9y^2}logseq____&amp;=\\\\sqrt{(x^2+3y)^2}=x^2+3y\\\\\\\\\\n\\\\sqrt {x + \\\\sqrt{x^2-y^2}}\\\\sqrt{x-\\\\sqrt{x^2-y^2}}logseq____&amp;=\\\\sqrt{\\\\left(x + \\\\sqrt{x^2-y^2}\\\\right)\\\\left(x-\\\\sqrt{x^2-y^2}\\\\right)}\\\\notag\\\\\\\\\\nlogseq____&amp;=\\\\sqrt{x^2-(x^2-y^2)}\\\\notag\\\\\\\\\\nlogseq____&amp;=\\\\sqrt{y^2}=\\\\left|y\\\\right|\\\\\\\\\\n\\\\sqrt[5]{a\\\\sqrt[3]a}=\\\\sqrt[5]{\\\\sqrt[3]{a^3}\\\\sqrt[3]a}\\nlogseq____&amp;=\\\\sqrt[5]{\\\\sqrt[3]{a^4}}\\n=\\\\sqrt[5]{a^\\\\frac43}\\n=a^{\\\\frac43\\\\frac15}=a^\\\\frac4{15}\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Flogseq____&quot;,71,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Vlogseq____&quot;,62,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-8b05-4956-9c07-1e405897636flogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Binomische Formeln]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Flogseq____&quot;,82,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Vlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Hlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-8ac3-49b3-a043-fff317445232logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[50,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;,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Flogseq____&quot;,52,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Vlogseq____&quot;,90,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,28,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-c8fb-495c-b9d4-31b2bfd46991logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{array}{c} (a+b)^0logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;1 \\\\\\\\\\n(a+b)^1logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;1 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^2logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 2 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^3logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;1 logseq____&amp;logseq____&amp; 3 logseq____&amp;logseq____&amp; 3 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^4logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 4 logseq____&amp;logseq____&amp; 6 logseq____&amp;logseq____&amp; 4 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^5logseq____&amp;logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 5 logseq____&amp;logseq____&amp; 10 logseq____&amp;logseq____&amp; 10 logseq____&amp;logseq____&amp; 5 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^6logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 6 logseq____&amp;logseq____&amp; 15 logseq____&amp;logseq____&amp; 20 logseq____&amp;logseq____&amp; 15 logseq____&amp;logseq____&amp; 6 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^7logseq____&amp;1 logseq____&amp;logseq____&amp; 7 logseq____&amp;logseq____&amp;21 logseq____&amp;logseq____&amp; 35 logseq____&amp;logseq____&amp; 35 logseq____&amp;logseq____&amp; \\\\cdots\\\\end{array}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Flogseq____&quot;,91,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Vlogseq____&quot;,91,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,25,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-9d62-4bcb-828a-2b4847c72ddelogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn } 10^x=y \\\\text{, dann}$\\n\\\\begin{align}\\nxlogseq____&amp;=\\\\lg y logseq____&amp; ,r\\\\\\\\\\nxlogseq____&amp;=\\\\log_y10logseq____&amp;,f\\\\\\\\\\nxlogseq____&amp;=\\\\log_{10}ylogseq____&amp;,r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&amp;= \\\\ln 2 logseq____&amp;, r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&amp;= \\\\ln 8 logseq____&amp;, f \\\\\\\\\\n\\\\ln 4 + \\\\ln 2 logseq____&amp;= \\\\ln 8 logseq____&amp;, r \\\\\\\\\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Flogseq____&quot;,90,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Vlogseq____&quot;,90,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,28,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-8f71-42da-b953-0eb0885e9973logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[53,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;,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Flogseq____&quot;,63,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Vlogseq____&quot;,80,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-1a60-45f4-bde0-2249a3e16e33logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Quadratische Gleichungen]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Flogseq____&quot;,62,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Vlogseq____&quot;,69,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ulogseq____&quot;,26,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Hlogseq____&quot;,26,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-fb01-4d31-b16f-ede50181733blogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nax^2+bx+clogseq____&amp;=0logseq____&amp;|:a\\\\quadlogseq____&amp;a\\\\ne0\\\\\\\\\\nx^2+\\\\frac ba x + \\\\frac ca logseq____&amp;= 0\\\\\\\\\\nplogseq____&amp;=\\\\frac ba,logseq____&amp;q = \\\\frac ca\\\\\\\\\\nx^2+px+qlogseq____&amp;=0\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Flogseq____&quot;,54,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Vlogseq____&quot;,54,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ulogseq____&quot;,26,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-4be9-4433-9ba7-402cede9ddeelogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel}$\\n\\\\begin{align}\\nx^4-34x^2+225logseq____&amp;=0\\\\\\\\\\n\\\\text{substituiert }ylogseq____&amp;=x^2\\\\\\\\\\ny^2-34y+225logseq____&amp;=0\\\\\\\\\\ny_{1,2}logseq____&amp;=17\\\\pm\\\\sqrt{(-17)^2-225}\\\\\\\\\\nlogseq____&amp;=17\\\\pm\\\\sqrt{289-225}\\nlogseq____&amp;=17\\\\pm\\\\sqrt{64}=17\\\\pm8\\\\\\\\\\nlogseq____&amp;=\\\\left.\\\\begin{cases}\\n25\\\\\\\\\\n9\\n\\\\end{cases}\\\\right|\\\\begin{array}{l}\\nx^2=25logseq____&amp;\\\\rightarrow logseq____&amp;x_1=5;logseq____&amp;x_2=-5\\\\\\\\\\nx^2=9logseq____&amp;\\\\rightarrow 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x=-\\\\frac{11}{12}\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Flogseq____&quot;,93,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Vlogseq____&quot;,93,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,27,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-5286-4009-afc2-fd2fe1ebbb89logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 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[[Wurzeln]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Flogseq____&quot;,60,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Vlogseq____&quot;,69,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Hlogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-c14d-40e4-a740-d7161bacaeealogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[63,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;,536870918]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Flogseq____&quot;,80,536870918]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Vlogseq____&quot;,80,536870918]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-79df-4066-9d9f-5553e2f6e8c0logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[64,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} = 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logseq____&amp;\\\\text{ falls } y\\\\ge0\\\\\\\\\\n-y logseq____&amp;\\\\text{ falls } 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[[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten 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}$[[Gleichungen]]$\\\\text{ sind richtig?}$\\n\\\\begin{align}\\ne^{x+y} logseq____&amp;= e^x + e^y logseq____&amp; ,f \\\\\\\\\\ne^{x+y} logseq____&amp;= e^x * x^y logseq____&amp; ,r \\\\\\\\\\ne^{x+y}logseq____&amp;=e^{xy} logseq____&amp; ,f\\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=x+y logseq____&amp; ,x+ylogseq____&gt;c 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um zu überprüfen, ob man eine Fallunterscheidung 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nn=a^1=a\\\\\\\\\\n\\\\sqrt[n]{\\\\frac ab} logseq____&amp;= \\\\frac{\\\\sqrt[n]a}{\\\\sqrt[n]b}\\\\\\\\\\n\\\\left(\\\\sqrt[n]a\\\\right)^mlogseq____&amp;=a^\\\\frac 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von Vieta]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&amp;=0 logseq____&amp;logseq____&amp; \\\\text{habe }x_{1,2}\\\\text{ als Lösung}\\\\\\\\\\nx_1+x_2logseq____&amp;=-p logseq____&amp;logseq____&amp; 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Gleichungen sind richtig?}$\\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;,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Flogseq____&quot;,92,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Vlogseq____&quot;,82,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-12b5-4936-990d-f9037eba2388logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Rationalmachen]] des [[Nenner]]slogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Flogseq____&quot;,65,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Vlogseq____&quot;,62,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,41,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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a,blogseq____&gt;0\\\\\\\\\\na^2b^2logseq____&amp;=(ab)^n\\\\\\\\\\n\\\\frac{a^n}{b^n}logseq____&amp;=\\\\left(\\\\frac ab\\\\right)^n\\\\\\\\\\na^na^mlogseq____&amp;=a^{n+m}\\\\\\\\\\n\\\\frac1{a^n}logseq____&amp;=a^{-n}\\\\\\\\\\n(a^n)^mlogseq____&amp;=a^{nm}\\\\\\\\\\na^0logseq____&amp;=1\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Flogseq____&quot;,60,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Vlogseq____&quot;,60,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-00ad-4f86-86c4-57dcba5cc68alogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Allgemein}$\\n\\\\begin{align}\\n(a+b)^2logseq____&amp;=a^2+2ab+b^2logseq____&amp;,\\\\text{ 1. 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#FIXMElogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Flogseq____&quot;,176,536870921]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Vlogseq____&quot;,176,536870921]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Ulogseq____&quot;,38,536870921]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Ulogseq____&quot;,149,536870921]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Hlogseq____&quot;,38,536870921]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Hlogseq____&quot;,149,536870921]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-18b9-4c61-b035-5ab07febefd4logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $f$ istlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Flogseq____&quot;,159,536870921]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Vlogseq____&quot;,159,536870921]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Ulogseq____&quot;,143,536870921]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-f182-48a5-8a1a-32ee59e205c9logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Kontradiktion]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Flogseq____&quot;,165,536870921]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Ulogseq____&quot;,143,536870921]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870921]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Hlogseq____&quot;,143,536870921]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-2318-4c10-b1df-43d702663193logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Flogseq____&quot;,179,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Vlogseq____&quot;,179,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Ulogseq____&quot;,136,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Ulogseq____&quot;,139,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Ulogseq____&quot;,140,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Ulogseq____&quot;,147,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Ulogseq____&quot;,154,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Hlogseq____&quot;,139,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Hlogseq____&quot;,140,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Hlogseq____&quot;,147,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Hlogseq____&quot;,154,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-3e73-4bc7-a5ec-a2b038359240logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Belegung]] (der Variablen)logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Flogseq____&quot;,176,536870921]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Ulogseq____&quot;,154,536870921]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870921]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Hlogseq____&quot;,154,536870921]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-69db-4b84-aec5-af3bfdc2f378logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\np\\\\land q\\\\lor r\\\\\\\\\\n(p\\\\land q)\\\\lor r\\\\\\\\\\np\\\\land (q\\\\lor r)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Flogseq____&quot;,174,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-16a7-4869-a227-42b122f21009logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Variable]], die den Wert $w$ oder $f$ annimmtlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Flogseq____&quot;,178,536870921]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Vlogseq____&quot;,178,536870921]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ulogseq____&quot;,137,536870921]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ulogseq____&quot;,146,536870921]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Hlogseq____&quot;,146,536870921]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-3382-4750-a592-8b24792e1085logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Weitere Beispiel}$\\n\\\\begin{align}\\n(p\\\\rightarrow q)logseq____&amp;\\\\equiv((\\\\neg q)\\\\rightarrow(\\\\neg p))\\\\\\\\\\n(p\\\\land(p\\\\rightarrow q)) logseq____&amp;\\\\rightarrow q logseq____&amp;\\\\quad \\\\text{Tantologie}\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Flogseq____&quot;,172,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-f032-46b0-8ce0-a59c344df65flogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Tantologie]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Flogseq____&quot;,179,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ulogseq____&quot;,142,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Hlogseq____&quot;,142,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-c4a0-47bb-b601-4284485a531flogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[166,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;,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Flogseq____&quot;,160,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Vlogseq____&quot;,179,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,136,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Hlogseq____&quot;,136,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-06a2-47dc-b1a2-f2ac5111cedalogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Büchertiplogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Flogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Vlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^17logseq____&quot;,false,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-9efb-417b-9cc7-602d1713e3b5logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[168,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;,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Flogseq____&quot;,177,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Vlogseq____&quot;,177,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,140,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Hlogseq____&quot;,140,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-4a86-4618-adf3-158baaea6b99logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Zuordnung von $w/f$ an jede [[Variable]] einer [[Aussageformel]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Flogseq____&quot;,161,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Vlogseq____&quot;,161,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,146,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,154,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Hlogseq____&quot;,146,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Hlogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-0ee6-4bee-ae3c-ca7a27f430f9logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Soweit die \\logseq____&quot;[[Syntax]]\\logseq____&quot;, jetzt die [[Semantik]]. Die [[Wahrheitswert]]e\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Flogseq____&quot;,162,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,140,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,144,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,147,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Hlogseq____&quot;,140,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Hlogseq____&quot;,144,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Hlogseq____&quot;,147,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Hlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-15a5-4859-9286-3e1d5ba32783logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formeln $p,q$ [[logisch äquivalent]], wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Flogseq____&quot;,159,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,136,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,145,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,153,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Hlogseq____&quot;,136,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Hlogseq____&quot;,145,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Hlogseq____&quot;,153,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-ee3d-406b-a7d5-639149342feclogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Flogseq____&quot;,171,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,142,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Hlogseq____&quot;,142,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-7a97-4d39-a245-72f606f2fa1dlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;C. Meinel, M. Mundhenk,  [[\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. Auflage 2011]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Flogseq____&quot;,167,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Vlogseq____&quot;,167,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,141,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Hlogseq____&quot;,141,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-f4dd-411d-afe4-c663e414a977logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[174,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;,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Flogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Hlogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-7aa9-4523-b637-d3acc0b6f542logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $w$ istlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Flogseq____&quot;,165,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Vlogseq____&quot;,165,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,142,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-e76d-4c92-9bbd-f56e544f8af9logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussageformel]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Flogseq____&quot;,178,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Hlogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-2e87-46d8-8e60-58eecfbcfdb7logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 1. [[Aussagen]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Flogseq____&quot;,167,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Vlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Hlogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-e897-4cf9-84bd-d1761149aab3logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussagenlogische variable]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Flogseq____&quot;,170,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,137,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Hlogseq____&quot;,137,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-ca5e-4c63-892f-bbf342b50a4alogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Flogseq____&quot;,161,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,136,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Hlogseq____&quot;,136,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Hlogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-f6a3-4805-a95e-3cd9fcf66d93logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\nlogseq____&amp;\\logseq____&quot;5\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;\\\\quadlogseq____&amp; (w)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;4\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;logseq____&amp; (f)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Jede gerade Zahl }\\\\ge4\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ ist Summe zweier Primzahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage, }w\\\\text{ oder }f)\\\\notag\\\\\\\\\\nlogseq____&amp;(\\\\text{Vermutung von Goldback 1742})\\\\text{, }logseq____&amp;logseq____&amp;\\\\text{richtig für gerade Zahlen bis }4*10^{18}\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Dieser Satz ist falsch}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{keine Aussage})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Gleichung } x^2+y^2=z^2 \\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ hat eine Lösung }x,y,z\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nlogseq____&amp;x^n+y^n=z^n\\\\text{ eine Lösung}logseq____&amp;logseq____&amp; (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nlogseq____&amp;x,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp;\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Gott ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Nietzsche ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Flogseq____&quot;,168,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Vlogseq____&quot;,177,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525d212-6417-4552-b812-87733f972f2elogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## 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gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____&gt;0$ welche keinen Sinn 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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 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Wissensabgleich [[Wurzeln]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Flogseq____&quot;,65,536870918]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Vlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870918]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^Hlogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[69,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-7ed2-4bf2-ad1e-be78827bd053logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel}$\\n$\\\\text{Welche quadratische Gleichung hat die Lösung}$\\n$x_1=3\\\\quad x_2=4$\\n\\\\begin{align}\\nx_1+x_2 = 7 logseq____&amp;= p logseq____&amp;, x_1x_2=12=q\\\\\\\\\\nx^2+px+qlogseq____&amp;=0\\\\\\\\\\nx^2-7x+12logseq____&amp;=0\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Flogseq____&quot;,79,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Vlogseq____&quot;,79,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,26,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,37,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,39,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df88-f4c9-4b78-863a-dafffe8b3fe7logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Flogseq____&quot;,81,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Vlogseq____&quot;,81,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,25,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,29,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,34,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Hlogseq____&quot;,34,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df88-6640-4819-8d56-7971f6cd4ca0logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Wurzeln]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Flogseq____&quot;,56,536870918]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Vlogseq____&quot;,45,536870918]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870918]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Hlogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df88-b42d-40c1-8311-75b2e9ba41aelogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche }$[[Gleichungen]]$\\\\text{ sind richtig?}$\\n\\\\begin{align}\\ne^{x+y} logseq____&amp;= e^x + e^y logseq____&amp; ,f \\\\\\\\\\ne^{x+y} logseq____&amp;= e^x * x^y logseq____&amp; ,r \\\\\\\\\\ne^{x+y}logseq____&amp;=e^{xy} logseq____&amp; ,f\\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=x+y logseq____&amp; ,x+ylogseq____&gt;c \\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=e^x*e^ylogseq____&amp;,f\\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=ln(e^x+y)logseq____&amp;,x+ylogseq____&gt;0\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Flogseq____&quot;,74,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Vlogseq____&quot;,74,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,30,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Hlogseq____&quot;,30,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-6103-49b0-9e1b-4051ab0b0de4logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Potenzen]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Flogseq____&quot;,67,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Vlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Hlogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-15d0-439d-ba78-afe6bf9ac78clogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Flogseq____&quot;,89,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Vlogseq____&quot;,89,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,38,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Hlogseq____&quot;,38,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-1e6a-42ec-99dd-22021324a828logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Binomische Formeln]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Flogseq____&quot;,58,536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Vlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Hlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-09d8-4506-856e-8b63f30ecda4logseq____&quot;,536870918]],[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;,536870918]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Flogseq____&quot;,76,536870918]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Vlogseq____&quot;,76,536870918]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[77,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-c5f3-41bb-b33d-75e37df11508logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[78,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;,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Flogseq____&quot;,69,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Vlogseq____&quot;,69,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-e153-4983-bc91-54bf798da838logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Satz von Vieta]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&amp;=0 logseq____&amp;logseq____&amp; \\\\text{habe }x_{1,2}\\\\text{ als Lösung}\\\\\\\\\\nx_1+x_2logseq____&amp;=-p logseq____&amp;logseq____&amp; x_1*x_2=q\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Flogseq____&quot;,59,536870918]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Vlogseq____&quot;,82,536870918]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,26,536870918]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,37,536870918]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Ulogseq____&quot;,39,536870918]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^Hlogseq____&quot;,37,536870918]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[79,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df88-7d16-4504-b37e-4d2202eb531clogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;![draws/2023-10-08-21-23-31.excalidraw](../assets/excalidraw_svg/2023-10-08-21-23-31.svg)logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Flogseq____&quot;,73,536870918]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Vlogseq____&quot;,74,536870918]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[80,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-0453-4858-bde6-c34d061aab70logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Binomialkoeffizient]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Flogseq____&quot;,63,536870918]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Vlogseq____&quot;,66,536870918]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,25,536870918]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,29,536870918]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[81,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[pq-Formel]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Flogseq____&quot;,52,536870918]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Vlogseq____&quot;,85,536870918]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,26,536870918]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Ulogseq____&quot;,39,536870918]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870918]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^Hlogseq____&quot;,39,536870918]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[82,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df88-e9ac-4d9d-9088-d5dbec52ce5alogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn } 10^x=y \\\\text{, dann}$\\n\\\\begin{align}\\nxlogseq____&amp;=\\\\lg y logseq____&amp; ,r\\\\\\\\\\nxlogseq____&amp;=\\\\log_y10logseq____&amp;,f\\\\\\\\\\nxlogseq____&amp;=\\\\log_{10}ylogseq____&amp;,r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&amp;= \\\\ln 2 logseq____&amp;, r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&amp;= \\\\ln 8 logseq____&amp;, f \\\\\\\\\\n\\\\ln 4 + \\\\ln 2 logseq____&amp;= \\\\ln 8 logseq____&amp;, r 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Schreibweise}$\\n\\\\begin{align}\\n\\\\text{cosa }logseq____&amp;\\\\text{plus }logseq____&amp;\\\\text{cubus }logseq____&amp;\\\\text{acq 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[[Quadratische Gleichungen]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Flogseq____&quot;,72,536870918]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Vlogseq____&quot;,45,536870918]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,26,536870918]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870918]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^Hlogseq____&quot;,26,536870918]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[85,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df88-5a4d-4b75-9671-d894d5d28947logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Flogseq____&quot;,63,536870918]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Vlogseq____&quot;,63,536870918]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,25,536870918]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,38,536870918]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Hlogseq____&quot;,38,536870918]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df88-84fe-45eb-9534-c991b8e756d9logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Einsetzen, um zu überprüfen, ob man eine Fallunterscheidung brauchtlogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Flogseq____&quot;,50,536870918]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Vlogseq____&quot;,54,536870918]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,27,536870918]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df88-86fc-4b43-9f8b-8da737b16aa0logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel}$\\n\\\\begin{align}\\nx^4-34x^2+225logseq____&amp;=0\\\\\\\\\\n\\\\text{substituiert }ylogseq____&amp;=x^2\\\\\\\\\\ny^2-34y+225logseq____&amp;=0\\\\\\\\\\ny_{1,2}logseq____&amp;=17\\\\pm\\\\sqrt{(-17)^2-225}\\\\\\\\\\nlogseq____&amp;=17\\\\pm\\\\sqrt{289-225}\\nlogseq____&amp;=17\\\\pm\\\\sqrt{64}=17\\\\pm8\\\\\\\\\\nlogseq____&amp;=\\\\left.\\\\begin{cases}\\n25\\\\\\\\\\n9\\n\\\\end{cases}\\\\right|\\\\begin{array}{l}\\nx^2=25logseq____&amp;\\\\rightarrow logseq____&amp;x_1=5;logseq____&amp;x_2=-5\\\\\\\\\\nx^2=9logseq____&amp;\\\\rightarrow logseq____&amp;x_1=3;logseq____&amp;x_2=-3\\\\\\\\\\n\\\\end{array}\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Flogseq____&quot;,79,536870918]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Vlogseq____&quot;,82,536870918]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,26,536870918]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,39,536870918]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df88-ecbb-4576-bf18-d96c2248e337logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[89,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;,536870918]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Flogseq____&quot;,43,536870918]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Vlogseq____&quot;,58,536870918]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-1b79-4ca9-a3eb-3503b5d278delogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Allgemein}$\\n\\\\begin{align}\\n\\\\ln a + \\\\ln b logseq____&amp;= \\\\ln(a*b) \\\\\\\\\\n\\\\ln(-a) logseq____&amp;= \\\\frac1{\\\\ln 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beliebige Variable\\ncubus -logseq____&gt; hoch 3logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Flogseq____&quot;,84,536870918]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Vlogseq____&quot;,84,536870918]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df88-0d4b-449a-9bd1-ed6ac6d57ce8logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[92,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} = 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[[Rationalmachen]] des [[Nenner]]slogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Flogseq____&quot;,61,536870918]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Xlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Vlogseq____&quot;,72,536870918]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,41,536870918]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Tabellenregeln]])logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Flogseq____&quot;,177,536870921]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Vlogseq____&quot;,177,536870921]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Ulogseq____&quot;,136,536870921]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Ulogseq____&quot;,139,536870921]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Ulogseq____&quot;,140,536870921]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Ulogseq____&quot;,147,536870921]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Ulogseq____&quot;,154,536870921]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Hlogseq____&quot;,139,536870921]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Hlogseq____&quot;,140,536870921]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Hlogseq____&quot;,147,536870921]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Hlogseq____&quot;,154,536870921]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-80d3-4e21-a0bf-6ae665c95800logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;C. Meinel, M. Mundhenk,  [[\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. 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logseq____&amp;logseq____&amp; (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nlogseq____&amp;x^n+y^n=z^n\\\\text{ eine Lösung}logseq____&amp;logseq____&amp; (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nlogseq____&amp;x,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp;\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Gott ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Nietzsche ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Flogseq____&quot;,180,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Vlogseq____&quot;,176,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-6ab9-439b-9498-edcca3c09a00logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sind $p$ und $q$ [[Aussagen]], so auch\\n\\\\begin{align}\\n(p\\\\land q) logseq____&amp;\\\\quadlogseq____&amp; (\\logseq____&quot;\\\\text{und}\\logseq____&quot;)\\\\\\\\\\n(p\\\\lor q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{oder}\\logseq____&quot;)\\\\\\\\\\n(\\\\neg p) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{nicht}\\logseq____&quot;)\\\\\\\\\\n(p\\\\rightarrow q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{impliziert}\\logseq____&quot;)\\\\\\\\\\n(p\\\\leftrightarrow q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{genau dann 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[[Tantologie]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Flogseq____&quot;,177,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Ulogseq____&quot;,142,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Hlogseq____&quot;,142,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-600d-4ade-8100-ede48a69bd78logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $w$ 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die den Wert $w$ oder $f$ annimmtlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Flogseq____&quot;,165,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Vlogseq____&quot;,165,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,137,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,146,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Hlogseq____&quot;,146,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-901b-4499-826b-97d5096530dalogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussagenlogische variable]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Flogseq____&quot;,167,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ulogseq____&quot;,137,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Hlogseq____&quot;,137,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-25fc-4553-bd29-cfca17b9dc84logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Flogseq____&quot;,170,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Vlogseq____&quot;,170,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,38,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,149,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Hlogseq____&quot;,38,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Hlogseq____&quot;,149,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-c22d-43b7-8d75-3636574a95b3logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Soweit die \\logseq____&quot;[[Syntax]]\\logseq____&quot;, jetzt die [[Semantik]]. Die [[Wahrheitswert]]e\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Flogseq____&quot;,158,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,140,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,144,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,147,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Hlogseq____&quot;,140,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Hlogseq____&quot;,144,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Hlogseq____&quot;,147,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Hlogseq____&quot;,151,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-a7a1-4c31-a4f7-94e648b3eb8dlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Büchertiplogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Flogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Vlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^17logseq____&quot;,false,536870921]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-be72-43c3-adc0-52b251b190fdlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Flogseq____&quot;,179,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,142,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Hlogseq____&quot;,142,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-6d92-4bad-9209-6e2cfef6aaedlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussageformel]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Flogseq____&quot;,165,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Hlogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-f7f6-4e6a-b4b3-da43a25bc3a9logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Weitere Beispiel}$\\n\\\\begin{align}\\n(p\\\\rightarrow q)logseq____&amp;\\\\equiv((\\\\neg q)\\\\rightarrow(\\\\neg p))\\\\\\\\\\n(p\\\\land(p\\\\rightarrow q)) logseq____&amp;\\\\rightarrow q logseq____&amp;\\\\quad \\\\text{Tantologie}\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Flogseq____&quot;,169,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-72c7-4a8a-8d22-f96a1aa9b51alogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[172,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;,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Flogseq____&quot;,156,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Vlogseq____&quot;,177,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,136,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Hlogseq____&quot;,136,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-028b-4db1-946f-dfed3b0f6156logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Zuordnung von $w/f$ an jede [[Variable]] einer [[Aussageformel]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Flogseq____&quot;,178,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Vlogseq____&quot;,178,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,146,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,154,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Hlogseq____&quot;,146,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Hlogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-42f0-4d02-8147-1f7ae55cf3e8logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Kontradiktion]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Flogseq____&quot;,162,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,143,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^Hlogseq____&quot;,143,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[174,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-baf8-4d6e-9947-6b64f09c7cadlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $f$ istlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Flogseq____&quot;,174,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Vlogseq____&quot;,174,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,143,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-b912-46ef-95da-34d361a7cd50logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 1. [[Aussagen]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Flogseq____&quot;,168,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Vlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Hlogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-37f7-45e5-8338-e00c9d842b5blogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Flogseq____&quot;,178,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Xlogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Vlogseq____&quot;,181,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,136,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,148,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,152,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Ulogseq____&quot;,155,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Hlogseq____&quot;,136,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Hlogseq____&quot;,150,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-95d6-431c-8a49-da7ddb849be8logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Belegung]] (der 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logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Hlogseq____&quot;,154,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6525df89-3e95-42d8-8757-a80119c9fd3dlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[179,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formeln $p,q$ [[logisch äquivalent]], wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv 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diff --git a/static/css/fonts/FiraCode-VariableFont_wght.ttf b/static/css/FiraCode-VariableFont_wght.ttf
similarity index 100%
rename from static/css/fonts/FiraCode-VariableFont_wght.ttf
rename to static/css/FiraCode-VariableFont_wght.ttf
diff --git a/static/css/fonts/Sora-VariableFont_wght.ttf b/static/css/Sora-VariableFont_wght.ttf
similarity index 100%
rename from static/css/fonts/Sora-VariableFont_wght.ttf
rename to static/css/Sora-VariableFont_wght.ttf
