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[[Wurzeln]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Flogseq____&quot;,107,536870921]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Vlogseq____&quot;,116,536870921]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Rationalmachen]] des [[Nenner]]slogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Flogseq____&quot;,108,536870921]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Vlogseq____&quot;,89,536870921]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,72,536870921]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,78,536870921]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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$\\\\sin^{-2}x+cos^2y=1,r$ ist 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[[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten 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\\\\\\\\\\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;,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Flogseq____&quot;,111,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Vlogseq____&quot;,111,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,61,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e477-fccf-4ef9-ab7e-33d878820187logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Wurzelgleichung]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Flogseq____&quot;,82,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Vlogseq____&quot;,116,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,63,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Hlogseq____&quot;,63,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e477-f2ed-4ca6-a74e-4bf8dd992968logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[127,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;,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Flogseq____&quot;,118,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Vlogseq____&quot;,118,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,64,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e477-807f-49f9-828c-fd031ff4edb1logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Binomische Formeln]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Flogseq____&quot;,101,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Vlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Hlogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e477-9c72-44cf-b570-51dfa85556fblogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[129,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;,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Flogseq____&quot;,128,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Vlogseq____&quot;,128,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e477-5e68-46d8-a8be-8a3d4d93115blogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\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;,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Flogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Vlogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e477-8db7-488b-bc5e-a93b5c6bdcfelogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\underbrace{\\\\frac6{2+\\\\sqrt2}*\\\\frac{2-\\\\sqrt2}{2-\\\\sqrt2}\\n= \\\\frac{6(2-\\\\sqrt2)}{2^2-(\\\\sqrt2)^2}}_\\\\text{3. binomische Formel}\\nlogseq____&amp;=\\\\frac{6(2-\\\\sqrt2)}2=3(2-\\\\sqrt2)\\\\\\\\\\n\\\\frac{a-b}{\\\\sqrt a+\\\\sqrt b}logseq____&amp;=\\\\frac{a-b}{\\\\sqrt a + \\\\sqrt b}\\\\frac{\\\\sqrt a-\\\\sqrt b}{\\\\sqrt a-\\\\sqrt b}logseq____&amp;, a,b,logseq____&gt;0\\\\notag\\\\\\\\\\n=\\\\frac{(a-b)(\\\\sqrt a-\\\\sqrt b)}{(a-b)}logseq____&amp;=\\\\sqrt a\\\\sqrt b\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Flogseq____&quot;,134,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Vlogseq____&quot;,134,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,72,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,78,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e477-c04f-4cc1-a5c8-0ad8f8df0a93logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\na^nlogseq____&amp;=\\\\underbrace{a*a*\\\\cdots*n}_n 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$\\\\rightarrow$ 5 ist abstand von x zu -3logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Flogseq____&quot;,216,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Xlogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Vlogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ulogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-938f-45d4-9cd8-fce473f0e950logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 1a}\\\\quad x\\\\ge -2$\\n\\\\begin{align}\\n|x+2|logseq____&amp;=x+2\\\\\\\\\\nx-3logseq____&amp;\\\\le x+2 logseq____&amp;|logseq____&amp;+3-x\\\\\\\\\\n0logseq____&amp;\\\\le5\\\\\\\\\\n\\\\end{align}\\n\\\\begin{align}\\nL_1=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|x\\\\ge3,x\\\\ge-2,0\\\\le5\\\\right\\\\}=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|x\\\\ge3\\\\right\\\\}=[3,\\\\infty)\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Flogseq____&quot;,172,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Xlogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Vlogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-36d6-47d4-a3be-9bed3dfb4dealogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Lösungsmenge der Gleichung }x^2+\\\\underbrace{4}_p x-\\\\underbrace{12}_q=0$\\n\\\\begin{align}\\nx_{1,2}logseq____&amp;=\\\\frac{-p}2\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}\\\\\\\\\\nlogseq____&amp;=-2\\\\pm\\\\sqrt{\\\\frac{16}4-(-12)}\\\\\\\\\\nlogseq____&amp;=-2\\\\pm4\\\\\\\\\\nLlogseq____&amp;=\\\\left\\\\{\\\\underbrace{x\\\\in\\\\Reals}_\\\\text{Name}\\\\middle|\\\\underbrace{x^2+4x-12=0}_\\\\text{Eigenschaft}\\\\right\\\\}\\\\\\\\\\nLlogseq____&amp;=\\\\left\\\\{2,-6\\\\right\\\\}\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Flogseq____&quot;,202,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Xlogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Vlogseq____&quot;,202,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ulogseq____&quot;,149,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-0922-4b6d-b897-0dd7681e2915logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Flogseq____&quot;,200,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Xlogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Vlogseq____&quot;,200,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Hlogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-0821-41df-9293-8629fd309b64logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nLlogseq____&amp;=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big||x-3|logseq____&lt;5\\\\right\\\\}=(-2,8)\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Flogseq____&quot;,181,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Xlogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Vlogseq____&quot;,170,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-469c-43eb-8b96-f0514af0650blogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 1}\\\\quad xlogseq____&lt;3$\\n\\\\begin{align}\\n|x-3|logseq____&amp;=-x+3\\\\\\\\\\n-x+3logseq____&amp;logseq____&lt;5 logseq____&amp;|logseq____&amp;-3\\\\\\\\\\n-xlogseq____&amp;logseq____&lt;2 logseq____&amp;|logseq____&amp;*-1\\\\\\\\\\nxlogseq____&amp;logseq____&gt;-2\\\\\\\\\\nL_1logseq____&amp;=(-2,3)\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Flogseq____&quot;,216,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Xlogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Vlogseq____&quot;,216,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-5b57-4bfb-9cf1-5a8e90c601balogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 3}\\\\quad xlogseq____&gt;3$\\n\\\\begin{align}\\nx+5logseq____&amp;logseq____&gt;0\\\\\\\\\\n|x+5|logseq____&amp;=x+5\\\\\\\\\\nx-3logseq____&amp;\\\\ge0\\\\\\\\\\n|x-3|logseq____&amp;=x-3\\\\\\\\\\nx+5logseq____&amp;logseq____&lt;2(x-3)\\\\\\\\\\nx+5logseq____&amp;logseq____&lt;2x-3 logseq____&amp;|logseq____&amp; -2x-5\\\\\\\\\\n-xlogseq____&amp;logseq____&lt;-11 logseq____&amp;|logseq____&amp; *(-1)\\\\\\\\\\nxlogseq____&amp;logseq____&gt;11\\n\\\\end{align}\\n\\\\begin{align}\\nL_3=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|xlogseq____&gt;3,xlogseq____&gt;11\\\\right\\\\}=(11,\\\\infty)\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Flogseq____&quot;,210,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Xlogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Vlogseq____&quot;,189,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-c113-474f-9830-16bc95b018f1logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Flogseq____&quot;,191,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Xlogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Vlogseq____&quot;,199,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Hlogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-2fdb-44b5-9f75-70751551b443logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 1} \\\\quad xlogseq____&lt;-5$\\n\\\\begin{align}\\nx+5logseq____&amp;logseq____&lt;0\\\\\\\\\\n|x+5|logseq____&amp;=-(x+5)=-x-5\\\\\\\\\\nx-3logseq____&amp;logseq____&lt;0\\\\\\\\\\n|x-3|logseq____&amp;=-(x-3)=-x+3\\\\\\\\\\n-x-5logseq____&amp;logseq____&lt; 2(-x+3)\\\\\\\\\\n-x-5logseq____&amp;logseq____&lt;-2x+6 logseq____&amp;|logseq____&amp;+5+2x\\\\\\\\\\nxlogseq____&lt;11\\\\\\\\\\n\\\\end{align}\\n\\\\begin{align}\\nL_1=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big|xlogseq____&lt;-5,x\\\\le11\\\\right\\\\}=(-\\\\infty,-5)\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Flogseq____&quot;,189,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Xlogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Vlogseq____&quot;,189,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-d970-4b55-b64c-dcae9e6bc305logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 1}\\\\quad x\\\\ge3$\\n\\\\begin{align}\\n|x-3|logseq____&amp;=x-3\\\\\\\\\\nx-3\\\\le|x+2|\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Flogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Xlogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Vlogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-6258-42f5-bfab-4f1f61b2cda4logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## 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Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Flogseq____&quot;,181,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Xlogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Vlogseq____&quot;,181,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^Ulogseq____&quot;,159,536870922]],[logseq____&quot;^15logseq____&quot;,[189,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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b Halbachsen der 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Lösung mit 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die den Wert $w$ oder $f$ annimmtlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Flogseq____&quot;,267,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Vlogseq____&quot;,267,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,224,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,231,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Hlogseq____&quot;,231,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-5282-4953-b8a4-7f0d3c243d16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[243,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Flogseq____&quot;,262,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Vlogseq____&quot;,262,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,227,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Hlogseq____&quot;,227,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-bd25-46aa-8147-bba143e5c578logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Flogseq____&quot;,250,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Vlogseq____&quot;,249,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,223,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,237,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Hlogseq____&quot;,223,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Hlogseq____&quot;,237,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-152e-4173-b541-d1dbae253afdlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Büchertiplogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Flogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Vlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^17logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-d558-4693-accc-3256ab1cc4aelogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wikipedia]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Flogseq____&quot;,268,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Vlogseq____&quot;,245,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,225,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Hlogseq____&quot;,225,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-02b2-4b49-be3c-a3014112fb58logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Flogseq____&quot;,244,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Vlogseq____&quot;,244,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,223,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,226,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,227,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,237,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,241,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Hlogseq____&quot;,226,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Hlogseq____&quot;,227,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Hlogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Hlogseq____&quot;,241,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-b29f-438c-a374-3e2b4e1125bclogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Flogseq____&quot;,258,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Vlogseq____&quot;,249,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,68,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Hlogseq____&quot;,68,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-9117-4b4f-b5cb-56298e0da77elogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Verknüpfung von Aussagen]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Flogseq____&quot;,264,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Vlogseq____&quot;,262,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,2],536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Hlogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-6b28-4e80-8aa4-7cf00391ea2blogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Belegung]] (der [[Variablen]])logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Flogseq____&quot;,254,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Vlogseq____&quot;,249,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,231,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,241,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Hlogseq____&quot;,231,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Hlogseq____&quot;,241,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-6d63-4668-ba61-575993317cb1logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Flogseq____&quot;,254,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Vlogseq____&quot;,254,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,75,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,237,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Hlogseq____&quot;,75,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Hlogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-22a0-4b4e-800d-9c3b1d94d5b2logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Tantologie]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Flogseq____&quot;,244,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Vlogseq____&quot;,249,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,229,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Hlogseq____&quot;,229,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-66dd-4c4d-91b5-e93b40007757logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $w$ istlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Flogseq____&quot;,252,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Vlogseq____&quot;,252,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,229,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-561a-4e02-aa7d-92ddcc83b234logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussageformel]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Flogseq____&quot;,267,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Vlogseq____&quot;,249,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,237,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Hlogseq____&quot;,237,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-0d6c-4656-8919-93637890d8eelogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Soweit die \\logseq____&quot;[[Syntax]]\\logseq____&quot;, jetzt die [[Semantik]]. Die [Wahrheitswerte]([[Wahrheitswert]])\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Flogseq____&quot;,248,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Vlogseq____&quot;,249,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,227,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,232,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Hlogseq____&quot;,227,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Hlogseq____&quot;,232,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Hlogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Hlogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-31d6-4609-b65f-f0e572b1a429logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[256,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Flogseq____&quot;,247,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Vlogseq____&quot;,244,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,223,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,237,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Hlogseq____&quot;,223,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-05c2-4536-a37a-40711ca3a1cblogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n(p\\\\rightarrow q)logseq____&amp;\\\\equiv((\\\\neg q)\\\\rightarrow(\\\\neg p))\\\\\\\\\\n(p\\\\land(p\\\\rightarrow q)) logseq____&amp;\\\\rightarrow q logseq____&amp;\\\\quad \\\\text{Tantologie}\\n\\\\end{align}logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Flogseq____&quot;,265,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Vlogseq____&quot;,265,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,68,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-a5d3-4009-a670-96419937b0d2logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[258,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;,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Flogseq____&quot;,249,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Vlogseq____&quot;,249,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Hlogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-7c15-4eb6-a1b1-f0095756e056logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Kontradiktion]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Flogseq____&quot;,252,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Vlogseq____&quot;,249,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,230,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Hlogseq____&quot;,230,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-bbba-4157-9a8d-1e3c326dc691logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formeln $p,q$ [logisch äquivalent]([[Logisch Äquivalent]]), wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Flogseq____&quot;,259,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Vlogseq____&quot;,249,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,223,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,233,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,240,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Hlogseq____&quot;,223,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Hlogseq____&quot;,233,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Hlogseq____&quot;,240,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-de34-4cf6-a683-aa85049d2e8dlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Flogseq____&quot;,260,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Vlogseq____&quot;,249,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,229,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Hlogseq____&quot;,229,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-6a2d-4227-8a57-1a77eb86beb0logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 1. [[Aussagen]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Flogseq____&quot;,245,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Vlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Hlogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-cff9-44e1-8678-19c8eeee7c3dlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $f$ istlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Flogseq____&quot;,259,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Vlogseq____&quot;,259,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,230,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-0898-45d5-a11c-d4b9de18157elogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[264,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? 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[[Beispiele]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Flogseq____&quot;,261,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Vlogseq____&quot;,249,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,68,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Hlogseq____&quot;,68,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-1fa6-4902-9cb7-577f3084b70flogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\np\\\\land 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[[Aussagenlogische Variable]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Flogseq____&quot;,255,536870924]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Xlogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Vlogseq____&quot;,249,536870924]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,220,536870924]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,224,536870924]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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Meinel, M. Mundhenk, [[\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. 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von $w/f$ an jede [Variable]([[Variablen]]) einer 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Bsp. $\\logseq____&quot;17logseq____&lt;y\\logseq____&quot;$logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Flogseq____&quot;,299,536870925]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Vlogseq____&quot;,299,536870925]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-b23e-4974-ae35-e945c856639clogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\logseq____&quot;\\\\text{x ist prim}\\logseq____&quot; \\\\quad logseq____&amp; \\\\text{ist AF mit Variablen x über den natürlichen Zahlen}\\\\\\\\\\n\\logseq____&quot;\\\\underbrace{x}_{x_1}logseq____&lt;\\\\underbrace{y}_{x_2}\\logseq____&quot;\\\\quad logseq____&amp;\\\\text{ist AF mit Variablen }x,y\\\\text{ über die reellen Zahlen } \\\\underbrace{\\\\Reals}_{U_1},\\\\underbrace{\\\\Reals}_{U_2}\\\\\\\\\\n\\logseq____&quot;\\\\text{x ist wahr}\\logseq____&quot;\\\\quadlogseq____&amp;\\\\text{ist AF mit Variablen x über dem Universum der 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x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist wahr}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Flogseq____&quot;,307,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Vlogseq____&quot;,307,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,279,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,283,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Hlogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-9634-4eb2-9773-7eb65a2a00aflogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Flogseq____&quot;,305,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Vlogseq____&quot;,319,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Hlogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-dc3e-403f-9db9-e7395f3aed96logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativschreibweisen:\\n$\\\\forall x: p(x)$ auch $\\\\bigwedge x:p(x)$\\n$\\\\exists x:p(x)$ auch $\\\\bigvee x:p(x)$logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Flogseq____&quot;,309,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Vlogseq____&quot;,319,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-714a-4448-8cf7-557c5b009ee0logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist falsch}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Flogseq____&quot;,300,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Vlogseq____&quot;,307,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&quot;,279,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&quot;,283,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Hlogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-4885-4e7c-95e3-58f46ccd88f1logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Regeln]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Flogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Vlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,271,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Jlogseq____&quot;,[],536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Hlogseq____&quot;,271,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^17logseq____&quot;,false,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-4346-40af-b3ae-22332b8c2a6clogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Satz]] mit [[Variablen]] $x_1,\\\\cdots,x_n$, der bei Ersetzung jedes $x_j$ durch ein [Objekt]([[Objekt (Logik)]]) aus $U_j$ stets zu einer [Aussage]([[Aussagen]]) wirdlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Flogseq____&quot;,316,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Vlogseq____&quot;,319,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,231,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,235,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,292,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,295,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Hlogseq____&quot;,231,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Hlogseq____&quot;,235,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Hlogseq____&quot;,292,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Hlogseq____&quot;,295,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-ef55-4902-81e2-f11db9522d3flogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Schachtelung von quantoren ([Beispiel]([[Beispiele]])):logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Flogseq____&quot;,318,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Vlogseq____&quot;,297,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,271,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Hlogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-cad4-4299-8dbc-e45b275910cdlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Betrachte $\\logseq____&quot;xlogseq____&lt;y\\logseq____&quot;$ als AF über $\\\\Reals, \\\\Reals$logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Flogseq____&quot;,325,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Vlogseq____&quot;,325,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,279,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,283,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-5bcf-472d-b92a-f8186a532ce9logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\underbrace{\\\\forall}_\\\\text{Allquantor} x: p(x) logseq____&amp;\\\\equiv p(O_1) \\\\land p(O_2) \\\\land \\\\cdots \\\\land p(O_m)\\\\\\\\\\n\\\\underbrace{\\\\exists}_\\\\text{Existenzquantor} x: p(x) logseq____&amp;\\\\equiv p(0_1) \\\\lor p(O_2) \\\\lor \\\\cdots \\\\lor p(0_m)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Flogseq____&quot;,311,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Vlogseq____&quot;,319,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-cfb0-4411-b692-cf6432282a8clogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\exists x:p(x)$ ist die Aussage: \\logseq____&quot;Es gibt (wenigstens) ein x aus U für das $p(x)$ wahr ist\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w \\\\quadlogseq____&amp;\\\\text{falls }p(x)\\\\text{ w ist für (wenigstens) ein x aus U}\\\\\\\\f\\\\quad logseq____&amp;\\\\text{falls }p(x)\\\\text{ f ist für alle x aus U}\\\\end{cases}$logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Flogseq____&quot;,308,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Vlogseq____&quot;,319,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,227,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Hlogseq____&quot;,227,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-71d1-4a16-af29-fa03fe4078b7logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Allquantor]] [[Existenzquantor]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Flogseq____&quot;,308,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Vlogseq____&quot;,308,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ulogseq____&quot;,284,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ulogseq____&quot;,290,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Hlogseq____&quot;,284,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Hlogseq____&quot;,290,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-df0a-430b-ba2f-f867618b9388logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Endliches Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Flogseq____&quot;,327,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Vlogseq____&quot;,319,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-2d40-4e69-8126-80c935c739c1logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Verschiedene [[Quantoren]] dürfen **nicht** vertauscht werdenlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Flogseq____&quot;,322,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Vlogseq____&quot;,331,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,279,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,283,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Hlogseq____&quot;,283,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-e5e8-4c5a-b9a2-024e58ff6c97logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x)$ AF in der Variablen $x$ über $U$:logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Flogseq____&quot;,299,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Vlogseq____&quot;,319,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-e65a-4bf6-9578-4b0034664876logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche Regeln]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Flogseq____&quot;,329,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Vlogseq____&quot;,329,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,272,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,280,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,287,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Hlogseq____&quot;,272,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Hlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Hlogseq____&quot;,280,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Hlogseq____&quot;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Hlogseq____&quot;,287,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Hlogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-b9ac-4437-a012-7c6b1268f66clogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Widerspruch = ↯, #logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Flogseq____&quot;,321,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Vlogseq____&quot;,321,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,279,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,283,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-dd00-4cc9-beef-e39cd99688e6logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Aussageform]] (AF) über [Universen]([[Universen (Logik)]]) $U_1,\\\\cdots,U_n$:logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Flogseq____&quot;,319,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Vlogseq____&quot;,319,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ulogseq____&quot;,293,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Hlogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Hlogseq____&quot;,293,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-00ad-4d40-9dbb-635e84630f5clogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\blacksquare$ = Beweisende, auch [q.e.d.]([[Q.E.D.]]), [[w.z.b.w.]], QED, ![image.png](../assets/image_1697192491775_0.png)logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Flogseq____&quot;,323,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Vlogseq____&quot;,323,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Ulogseq____&quot;,273,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Ulogseq____&quot;,276,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Ulogseq____&quot;,279,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Ulogseq____&quot;,283,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Hlogseq____&quot;,273,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Hlogseq____&quot;,276,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-56e4-4b5c-94b0-52ee4df75a57logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:(p(x)\\\\land q(x)) logseq____&amp;\\\\equiv (\\\\forall x: p(x)) \\\\land (\\\\forall x:q(x));\\\\notag\\\\\\\\\\n\\\\exists x: (p(x) \\\\lor q(x)) logseq____&amp;\\\\equiv (\\\\exists x: p(x))\\\\lor(\\\\exists x: q(x)),\\\\quadlogseq____&amp;\\\\text{Große Assoziativgesetze}\\\\\\\\\\n\\\\neg(\\\\forall x:p(x))logseq____&amp;\\\\equiv \\\\exists x: (\\\\neg p(x));\\\\quadlogseq____&amp;\\\\text{Große de Morgansche Regeln;}\\\\notag\\\\\\\\\\n\\\\neg(\\\\exists x: p(x)) logseq____&amp;\\\\equiv \\\\forall x: (\\\\neg p(x)),\\\\quadlogseq____&amp;\\\\text{Negationsregeln.}\\n\\\\end{align}logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Flogseq____&quot;,297,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Vlogseq____&quot;,297,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,271,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-c95c-46f5-8254-62c967373928logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Aussageform]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Flogseq____&quot;,329,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Vlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Jlogseq____&quot;,[],536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Hlogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-9d36-40a3-b7af-317563d9f711logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXMElogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Flogseq____&quot;,302,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Vlogseq____&quot;,302,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Ulogseq____&quot;,75,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Hlogseq____&quot;,75,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-3678-466f-88b0-26cf3cf73e26logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Wäre $y$ aus $\\\\Reals$ mit $xlogseq____&lt;y$ für alle $x$ aus $\\\\Reals$, so insbesondere auch $ylogseq____&lt;y$, Widerspruch. $\\\\blacksquare$logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Flogseq____&quot;,303,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Vlogseq____&quot;,303,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ulogseq____&quot;,279,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ulogseq____&quot;,283,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-c349-45e7-825c-38d5cbce2c14logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;wobei $\\\\pi$ eine \\logseq____&quot;[[Permutation]]\\logseq____&quot; der Zahl $(1,2,\\\\cdots,n)$ istlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Flogseq____&quot;,331,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Vlogseq____&quot;,331,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ulogseq____&quot;,279,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ulogseq____&quot;,283,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ulogseq____&quot;,285,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Hlogseq____&quot;,285,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-ce63-4403-8b40-3114b631d0e3logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $x$ aus $\\\\Reals$ beliebig. Setze $y:=x+1$ (ist aus $\\\\Reals$). Dann ist $xlogseq____&lt;x+1=y$ also $xlogseq____&lt;y$. $\\\\blacksquare$logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Flogseq____&quot;,300,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Vlogseq____&quot;,300,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ulogseq____&quot;,279,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ulogseq____&quot;,283,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-abfb-4df5-bbdb-fdaf0d252815logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Flogseq____&quot;,318,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Vlogseq____&quot;,318,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Ulogseq____&quot;,271,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Ulogseq____&quot;,274,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Ulogseq____&quot;,286,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Ulogseq____&quot;,291,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Hlogseq____&quot;,274,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Hlogseq____&quot;,286,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Hlogseq____&quot;,291,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-a52f-417d-a9af-a8ffe33f46a5logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Flogseq____&quot;,331,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Vlogseq____&quot;,296,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ulogseq____&quot;,279,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ulogseq____&quot;,283,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Hlogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-6484-4608-b1a2-450ead187333logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Die beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der [[Aussagenlogik]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Flogseq____&quot;,313,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Vlogseq____&quot;,319,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Ulogseq____&quot;,275,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Ulogseq____&quot;,294,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Hlogseq____&quot;,275,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Hlogseq____&quot;,294,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-a90d-483c-8097-1e36f13c71b3logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Für das leere Universum gilt\\n\\\\begin{align}\\n\\\\forall x: p(x)\\\\quadlogseq____&amp;Tautologie\\\\\\\\\\n\\\\exists x: p(x)\\\\quadlogseq____&amp;Kontradiktion\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Flogseq____&quot;,326,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Vlogseq____&quot;,319,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-216e-48a1-b6af-7de21b128259logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[328,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\forall x:p(x)$ ist die [Aussage]([[Aussagen]]): $\\logseq____&quot;\\\\text{Für alle x aus U ist p(x) wahr}\\logseq____&quot;\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w\\\\quadlogseq____&amp;\\\\text{fallls p(x) w für alle x aus U}\\\\\\\\f\\\\quadlogseq____&amp;\\\\text{falls p(x) f für (wenigstens) ein x aus U}\\\\end{cases}$logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[328,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[328,logseq____&quot;^Flogseq____&quot;,313,536870925]],[logseq____&quot;^15logseq____&quot;,[328,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[328,logseq____&quot;^Vlogseq____&quot;,313,536870925]],[logseq____&quot;^15logseq____&quot;,[328,logseq____&quot;^Ulogseq____&quot;,227,536870925]],[logseq____&quot;^15logseq____&quot;,[328,logseq____&quot;^Ulogseq____&quot;,235,536870925]],[logseq____&quot;^15logseq____&quot;,[328,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[328,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[328,logseq____&quot;^Hlogseq____&quot;,227,536870925]],[logseq____&quot;^15logseq____&quot;,[328,logseq____&quot;^Hlogseq____&quot;,235,536870925]],[logseq____&quot;^15logseq____&quot;,[328,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[328,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-0cdd-4e41-9bf1-063d70c28d08logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n(p\\\\land q)\\\\land r logseq____&amp;\\\\equiv p\\\\land(q\\\\land r),\\\\quadlogseq____&amp;\\\\text{schreibe daher: } p\\\\land q\\\\land r,\\\\quad \\\\land \\\\text{ assoziativ}\\\\\\\\\\n(p \\\\lor q) \\\\lor r logseq____&amp;\\\\equiv p \\\\lor (q\\\\lor r),\\\\quadlogseq____&amp;\\\\text{schreibe daher: } p\\\\lor q\\\\lor r,\\\\quad \\\\lor \\\\text{ assoziativ}\\\\\\\\\\np \\\\land q logseq____&amp;\\\\equiv q \\\\land p,\\\\quad \\\\land logseq____&amp;\\\\text{ kommutativ}\\\\\\\\\\np \\\\lor q logseq____&amp;\\\\equiv q \\\\lor p,\\\\quad \\\\lor logseq____&amp;\\\\text{ kommutativ}\\\\\\\\\\n\\\\neg(\\\\neg p) logseq____&amp;\\\\equiv p, \\\\quad \\\\neg logseq____&amp;\\\\text{ idenpotent}\\\\\\\\\\np\\\\land(q\\\\lor r)logseq____&amp;\\\\equiv (p\\\\land q)\\\\lor(p\\\\land r);\\\\notag\\\\\\\\\\np\\\\lor(q\\\\land r)logseq____&amp;\\\\equiv (p\\\\lor q)\\\\lor(p\\\\land r),\\\\quad logseq____&amp;\\\\land,\\\\lor\\\\text{ wechselseitig distributiv}\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&amp;\\\\equiv(\\\\neg p)\\\\lor(\\\\neg q);\\\\notag\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&amp;\\\\equiv(\\\\neg p)\\\\land (\\\\neg q), \\\\quad logseq____&amp;\\\\text{ (kleine) de Morgansche Regeln}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^Flogseq____&quot;,304,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^Vlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[329,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-e7eb-4f42-bedd-1b0806685f38logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nlogseq____&amp;\\\\neg\\\\left(\\\\forall x :\\\\exists y :\\\\forall w :\\\\forall u :\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)\\\\right)\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x:(\\\\neg(\\\\exists y: \\\\forall w: \\\\forall u: \\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x:\\\\forall y:(\\\\neg(\\\\forall w: \\\\forall u:\\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x:\\\\forall y:\\\\exists w:(\\\\neg(\\\\forall u:\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x: \\\\forall y: \\\\exists w: \\\\exists u : \\\\forall z:\\\\neg(p(x,y,z)\\\\rightarrow q(u,w))\\n\\\\end{align}logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^Flogseq____&quot;,333,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^Vlogseq____&quot;,333,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[330,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-efd5-4c84-8233-13fa8410798blogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nlogseq____&amp;\\\\forall x: \\\\forall y: p(x, y) \\\\equiv \\\\forall y: \\\\forall x: p(x,y)\\\\\\\\\\nlogseq____&amp;\\\\exists x:\\\\exists y:p(x,y)\\\\equiv\\\\exists y:\\\\exists x:p(x,y)\\\\\\\\\\nlogseq____&amp;[\\\\forall x_1:\\\\forall x_2: \\\\cdots:\\\\forall x_n:p(x_1,x_2,\\\\cdots,x_n)\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\equiv\\\\forall_{x_{\\\\pi(1)}}:\\\\forall_{x_{\\\\pi(1)}}:\\\\cdots:\\\\forall_{x_{\\\\pi(1)}}:p(x_1,x_2,\\\\cdots,x_n)\\n\\\\end{align}logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^Flogseq____&quot;,296,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^Xlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^Vlogseq____&quot;,296,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^Ulogseq____&quot;,279,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^Ulogseq____&quot;,283,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[331,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531e478-d24a-49e5-8e0e-f4a1b2f4384clogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[332,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x,y)$ AF in Variablen $x,y$ über $U_1,U_2$\\n\\\\begin{align}\\n\\\\underbrace{\\\\forall x: \\\\underbrace{\\\\exists y: p(x,y)}_{\\\\text{AF in den Variablen }x\\\\text{ über 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