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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;,[96,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Flogseq____&quot;,106,536870921]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Vlogseq____&quot;,106,536870921]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-9dbe-4e45-85d1-d863f674590alogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Häufige Falle:}$\\n\\\\begin{align}\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&amp;=(-1)^\\\\frac22logseq____&amp;=(-1)^1logseq____&amp;=-1\\\\\\\\\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&amp;=1^\\\\frac12logseq____&amp;logseq____&amp;=1\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Flogseq____&quot;,122,536870921]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Vlogseq____&quot;,137,536870921]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-4f5c-4d9f-a287-f5f196dd4f90logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n(a+b)^3(a^2+b^2)^3(a-b)^3logseq____&amp;=(a^2+b^2)^3\\\\left((a+b)(a-b)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=(a^2+b^2)^3(a^2-b^2)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=\\\\left((a^2+b^2)(a^2-b^2)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=(a^4-b^4)^3\\\\\\\\\\n\\\\frac{a-b}{(a+b)^{-1}}logseq____&amp;=(a-b)(a+b)\\\\notag\\\\\\\\\\nlogseq____&amp;=a^2-b^2\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Flogseq____&quot;,86,536870921]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Vlogseq____&quot;,86,536870921]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-554d-488b-aaa2-76963b971408logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 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3}\\n\\\\\\\\\\n\\\\cdots\\n\\\\end{array}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Flogseq____&quot;,119,536870921]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Vlogseq____&quot;,95,536870921]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Ulogseq____&quot;,61,536870921]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Ulogseq____&quot;,65,536870921]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-32ff-44f3-9beb-e10882add026logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Flogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Vlogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Ulogseq____&quot;,69,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Ulogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Hlogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-4e8b-4f4d-b47a-4a277036b21blogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[102,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;,[102,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Flogseq____&quot;,94,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Vlogseq____&quot;,94,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Ulogseq____&quot;,72,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Ulogseq____&quot;,78,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-c061-45ae-ad3f-a718ee5eaac3logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Pascalsches Dreieck]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Flogseq____&quot;,82,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Vlogseq____&quot;,106,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Ulogseq____&quot;,61,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,2],536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Hlogseq____&quot;,61,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-a917-4286-8455-a77b003be4d7logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche }$[[Gleichungen]]$\\\\text{ sind richtig?}$\\n\\\\begin{align}\\ne^{x+y} logseq____&amp;= e^x + e^y logseq____&amp; ,f \\\\\\\\\\ne^{x+y} logseq____&amp;= e^x * x^y logseq____&amp; ,r \\\\\\\\\\ne^{x+y}logseq____&amp;=e^{xy} logseq____&amp; ,f\\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=x+y logseq____&amp; ,x+ylogseq____&gt;c \\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=e^x*e^ylogseq____&amp;,f\\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=ln(e^x+y)logseq____&amp;,x+ylogseq____&gt;0\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^Flogseq____&quot;,118,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^Vlogseq____&quot;,118,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^Ulogseq____&quot;,66,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^Hlogseq____&quot;,66,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-aee8-4956-a92e-86d44d59d858logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wolframalpha]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^Flogseq____&quot;,115,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^Vlogseq____&quot;,115,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^Ulogseq____&quot;,77,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^Ulogseq____&quot;,79,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^Hlogseq____&quot;,79,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-9bcb-4f52-93a9-fd92d4eb63e6logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Binomische Formeln]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Flogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Vlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Hlogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-507a-4a36-b43a-cdc82e464a4clogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\frac12 \\\\sqrt2, \\\\frac12, \\\\frac12\\\\sqrt3 \\\\text{ sind werte von }\\\\sin x$\\n\\\\begin{align}\\n\\\\sin 30\\\\degreelogseq____&amp;=\\\\frac12\\\\\\\\\\n\\\\sin 45\\\\degree logseq____&amp;= \\\\frac12\\\\sqrt2 \\\\\\\\\\n\\\\sin 60\\\\degree logseq____&amp;= \\\\frac12 \\\\sqrt3 \\\\\\\\\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^Flogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^Vlogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^Ulogseq____&quot;,69,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-ac0d-4ac7-be2e-34ca264b0d6alogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Alte 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}logseq____&amp;6\\\\\\\\\\nxlogseq____&amp;+logseq____&amp;x^3logseq____&amp;=logseq____&amp;6\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Flogseq____&quot;,86,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Vlogseq____&quot;,130,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-6332-43bf-b72e-1132742b5ef7logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\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;,[109,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Flogseq____&quot;,88,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Vlogseq____&quot;,88,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Ulogseq____&quot;,64,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-d4fc-4f61-8e0e-51154d519f5dlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Einsetzen, um zu überprüfen, ob man eine Fallunterscheidung brauchtlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Flogseq____&quot;,131,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Vlogseq____&quot;,124,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ulogseq____&quot;,63,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-4141-40b6-a0b9-f214bae5bb76logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])\\n\\\\begin{align}\\nx^4-34x^2+225logseq____&amp;=0\\\\\\\\\\n\\\\text{substituiert 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logseq____&amp;x_1=3;logseq____&amp;x_2=-3\\\\\\\\\\n\\\\end{array}\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Flogseq____&quot;,135,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Vlogseq____&quot;,136,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Ulogseq____&quot;,62,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Ulogseq____&quot;,76,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Hlogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-4a75-4a70-b664-c80b1b5da4cdlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\n\\\\tan x logseq____&amp;= \\\\frac{\\\\sin x}{\\\\cos x} logseq____&amp;, \\\\cos x \\\\ne 0\\\\\\\\\\n\\\\sin^{-2}x-\\\\cos^2xlogseq____&amp;=1logseq____&amp;,f\\\\\\\\\\n\\\\sin x = \\\\cos x logseq____&amp;= 1 logseq____&amp;, f\\\\\\\\\\n\\\\sin^{-2}x+cos^2ylogseq____&amp;=1logseq____&amp;,r\\\\\\\\\\n1+tan^2xlogseq____&amp;=\\\\frac1{\\\\cos^2x}logseq____&amp;,\\\\cos 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[[Quadratische Gleichungen]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Flogseq____&quot;,127,536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Vlogseq____&quot;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Ulogseq____&quot;,62,536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Hlogseq____&quot;,62,536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-2813-4638-ae0c-b711a045df1flogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\na^nlogseq____&amp;=\\\\underbrace{a*a*\\\\cdots*n}_n logseq____&amp; a,blogseq____&gt;0\\\\\\\\\\na^2b^2logseq____&amp;=(ab)^n\\\\\\\\\\n\\\\frac{a^n}{b^n}logseq____&amp;=\\\\left(\\\\frac 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[[Links]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Flogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Vlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Ulogseq____&quot;,77,536870921]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Hlogseq____&quot;,77,536870921]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^17logseq____&quot;,false,536870921]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-1eb0-4989-949f-a94fb424a174logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____&gt;0$ welche keinen Sinn ergibtlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Flogseq____&quot;,123,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Vlogseq____&quot;,125,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Ulogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Hlogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-174b-458e-ad31-f1fcf2a4eb14logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[117,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n(2x+y)^4logseq____&amp;=(2x)^4+4*(2x)^3y+6*(2x)^2y^2+4*2xy^3+y^4\\\\notag\\\\\\\\\\nlogseq____&amp;=16x^4+32x^3y+24x^2y^2+8xy^3+y^4\\\\\\\\\\n(1+\\\\sqrt 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x)^5logseq____&amp;=2+20x+40x^2\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[117,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[117,logseq____&quot;^Flogseq____&quot;,84,536870921]],[logseq____&quot;^15logseq____&quot;,[117,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[117,logseq____&quot;^Vlogseq____&quot;,84,536870921]],[logseq____&quot;^15logseq____&quot;,[117,logseq____&quot;^Ulogseq____&quot;,61,536870921]],[logseq____&quot;^15logseq____&quot;,[117,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[117,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[117,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[117,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[117,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-c090-4426-bb26-e74053dbc9fdlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Potenzen]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Flogseq____&quot;,115,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Vlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Hlogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-5821-46e6-a921-61ee16244ee5logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Flogseq____&quot;,95,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Vlogseq____&quot;,95,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Ulogseq____&quot;,61,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Ulogseq____&quot;,65,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Ulogseq____&quot;,71,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Hlogseq____&quot;,71,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-d0cd-4094-8b7e-ce98d17630aalogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Potenzen]] und [[Wurzeln]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Flogseq____&quot;,106,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Vlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Hlogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Hlogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-88d9-4b7c-9eed-39e38eb09a0dlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nax^2+bx+clogseq____&amp;=0logseq____&amp;|:a\\\\quadlogseq____&amp;a\\\\ne0\\\\\\\\\\nx^2+\\\\frac ba x + \\\\frac ca logseq____&amp;= 0\\\\\\\\\\nplogseq____&amp;=\\\\frac ba,logseq____&amp;q = \\\\frac ca\\\\\\\\\\nx^2+px+qlogseq____&amp;=0\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Flogseq____&quot;,113,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Vlogseq____&quot;,113,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,62,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-08c9-45d0-9941-d154bd1834a3logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn }alogseq____&gt;0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=a\\\\sqrt{a}logseq____&amp;,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=a^2-\\\\sqrt{a}logseq____&amp;,f\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=\\\\sqrt{a^3}logseq____&amp;,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=a^{\\\\frac32}logseq____&amp;,r\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Flogseq____&quot;,137,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Vlogseq____&quot;,137,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-d7a4-4f13-8aa6-52d3d73554e5logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[123,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;,[123,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Flogseq____&quot;,125,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Vlogseq____&quot;,125,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-aa9d-4d23-bf90-9f1a3d6ea3a2logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Wurzelgleichung]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Flogseq____&quot;,113,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Vlogseq____&quot;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,63,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Hlogseq____&quot;,63,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-2596-4a29-94ff-0071ab7d9acdlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]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;,133,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Vlogseq____&quot;,127,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Hlogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-e007-4abd-ac16-78b9ac107fa0logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Wenn }alogseq____&gt;0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac b{\\\\sqrt a} = \\\\frac b{\\\\sqrt a}*\\\\frac{\\\\sqrt a}{\\\\sqrt a} = \\\\frac {b\\\\sqrt a}a\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Flogseq____&quot;,81,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Vlogseq____&quot;,81,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,72,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,78,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-9cb6-4de5-a872-5aba47396d9elogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Wurzeln]]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;,130,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Vlogseq____&quot;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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3logseq____&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;,108,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Vlogseq____&quot;,108,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-d6a4-40b4-9714-cdcbc74a4fa3logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Die Lösung von } x^n-a=0 \\\\text{ ist } x=\\\\sqrt[n]a$ #FIXME ich glaube hier fehlt logseq____&gt;0 constraintlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Flogseq____&quot;,127,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Vlogseq____&quot;,127,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Hlogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-563f-4392-afa3-0934b6f99929logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Potenzen]]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;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Vlogseq____&quot;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[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;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Hlogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-fe9d-449a-80f7-e6bd8d174481logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\sqrt{a+5}-\\\\sqrt{x+3}logseq____&amp;=2\\\\sqrt(x+1) logseq____&amp;|logseq____&amp;()^2\\\\\\\\\\n\\\\left(\\\\sqrt{x+5}-\\\\sqrt{x+3}\\\\right)^2logseq____&amp;=4(x+1)\\\\\\\\\\n(x+5)-2\\\\sqrt{x+5}\\\\sqrt{x+3}+(x+3)logseq____&amp;=4x+4logseq____&amp;|logseq____&amp;-(2x+8)\\\\\\\\\\n-2\\\\sqrt{(x+5)(x+3)}logseq____&amp;=2x-4 logseq____&amp;|logseq____&amp;()^2\\\\\\\\\\n4(x+5)(x+3)logseq____&amp;=4x^2-16x+16\\\\\\\\\\n4x^2+32x+60logseq____&amp;=4x^2-16x+16logseq____&amp;|logseq____&amp;-4x^2+16x-16\\\\\\\\\\n48x+44logseq____&amp;=0\\\\quad x=-\\\\frac{11}{12}\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Flogseq____&quot;,124,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Vlogseq____&quot;,124,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,63,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82c-33e3-4a5b-ac05-35d5443a553clogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Trigonometrie]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Flogseq____&quot;,99,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Vlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Ulogseq____&quot;,69,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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Lösung mit 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2}\\\\quad 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[[Ellipse]] nur statt [[Summe]] 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[[Ellipse]]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;,181,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Xlogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Vlogseq____&quot;,174,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,143,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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b Halbachsen der 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[[Betrag]] ist der zu [[Abstand]] 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Lösung mit 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logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,2],536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Hlogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-3905-4140-a7bd-3d9b06900303logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wikipedia]]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;,259,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Vlogseq____&quot;,256,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,224,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Hlogseq____&quot;,224,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-acc0-49a0-baa5-d4e89e3ae7f6logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Weitere [[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;,264,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Vlogseq____&quot;,246,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,68,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[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;~u6531c82d-4bf6-4edf-a46f-b40f69da6c27logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[249,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;,[249,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Flogseq____&quot;,248,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Vlogseq____&quot;,248,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,68,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-c3c0-4468-85bf-15722e2036e7logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[250,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;,[250,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Flogseq____&quot;,242,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Vlogseq____&quot;,265,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,222,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Hlogseq____&quot;,222,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-0c4a-452c-8045-f3f808c5dda1logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[251,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;,[251,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Flogseq____&quot;,253,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Vlogseq____&quot;,253,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,226,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Hlogseq____&quot;,226,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-ad88-4905-bcc5-d0719e2e56balogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[252,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;,[252,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Flogseq____&quot;,246,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Vlogseq____&quot;,246,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Hlogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-4311-4411-a70a-cbe40261dff3logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 1. [[Aussagen]]logseq____&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;,256,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Vlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Hlogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-9580-4221-a71a-d53155dbd0bflogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[254,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;,[254,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Flogseq____&quot;,243,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Vlogseq____&quot;,246,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,226,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,231,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,233,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,237,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Hlogseq____&quot;,226,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Hlogseq____&quot;,231,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Hlogseq____&quot;,233,536870924]],[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;~u6531c82d-0f88-492b-bcf6-7a02d1a67cdalogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussageformel]]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;,257,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Vlogseq____&quot;,246,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Hlogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-b630-4602-b001-2d01adbc1962logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Büchertiplogseq____&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;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Vlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^17logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-cd3e-4c5e-bf3a-8137ca3bfa76logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussagenlogische Variable]]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;,254,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Vlogseq____&quot;,246,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,223,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Hlogseq____&quot;,223,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-e191-4bf4-a7a8-23cffb063c89logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Tantologie]]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;,265,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Vlogseq____&quot;,246,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,228,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^Hlogseq____&quot;,228,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[258,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-af57-4ff8-930f-9da35664e478logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;C. Meinel, M. Mundhenk, [[\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. Auflage 2011]]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;,256,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Vlogseq____&quot;,256,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Ulogseq____&quot;,227,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^Hlogseq____&quot;,227,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[259,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-b3e0-4cdb-a704-1034da0c9f69logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Belegung]] (der [[Variablen]])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;,255,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Vlogseq____&quot;,246,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,230,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Ulogseq____&quot;,240,536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[260,logseq____&quot;^Hlogseq____&quot;,230,536870924]],[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;~u6531c82d-c045-456c-9403-53ea5f0e52a2logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[261,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;,[261,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Flogseq____&quot;,241,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Vlogseq____&quot;,246,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,222,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,232,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Hlogseq____&quot;,222,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Hlogseq____&quot;,232,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^Hlogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[261,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-47e6-412c-90d4-86b5baa68f4clogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\nlogseq____&amp;\\logseq____&quot;5\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;\\\\quadlogseq____&amp; (w)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;4\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;logseq____&amp; (f)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Jede gerade Zahl }\\\\ge4\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ ist Summe zweier Primzahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage, }w\\\\text{ oder }f)\\\\notag\\\\\\\\\\nlogseq____&amp;(\\\\text{Vermutung von Goldback 1742})\\\\text{, }logseq____&amp;logseq____&amp;\\\\text{richtig für gerade Zahlen bis }4*10^{18}\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Dieser Satz ist falsch}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{keine Aussage})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Gleichung } x^2+y^2=z^2 \\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ hat eine Lösung }x,y,z\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nlogseq____&amp;x^n+y^n=z^n\\\\text{ eine Lösung}logseq____&amp;logseq____&amp; (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nlogseq____&amp;x,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp;\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Gott ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Nietzsche ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Flogseq____&quot;,251,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Vlogseq____&quot;,253,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-6a5c-4ede-a100-7d445456f7f3logseq____&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;,241,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Vlogseq____&quot;,241,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,229,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[263,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-b048-4448-a546-0b5015e4e3f5logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Flogseq____&quot;,261,536870924]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Vlogseq____&quot;,246,536870924]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,228,536870924]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^Hlogseq____&quot;,228,536870924]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[264,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-a242-4496-9ee9-4dae5be7844blogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]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;,260,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Vlogseq____&quot;,246,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,222,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Hlogseq____&quot;,222,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Hlogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-6fed-40c0-a6c6-069177061b5clogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $w$ istlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Flogseq____&quot;,258,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Vlogseq____&quot;,258,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,228,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-8e4c-4805-81c1-4be8826a8b5elogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Zuordnung von $w/f$ an jede [Variable]([[Variablen]]) einer 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$U$: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;,297,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Vlogseq____&quot;,303,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-0726-4ec4-899b-935d380d009dlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 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logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Jlogseq____&quot;,[],536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Hlogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-6671-4ba6-9fe1-11e1df65d73elogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[304,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;,[304,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Flogseq____&quot;,296,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Vlogseq____&quot;,296,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-415b-470a-8805-00f874aba20blogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[305,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;,[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;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Vlogseq____&quot;,316,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-6c46-4d03-bebb-060b6be75547logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Endliches Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$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;,320,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Vlogseq____&quot;,303,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-fc76-415f-866a-d2dbf99ff818logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[307,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;,[307,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Flogseq____&quot;,327,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Vlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-52d3-450d-bb4b-d88f2cbb5367logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[308,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;,[308,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Flogseq____&quot;,301,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Vlogseq____&quot;,303,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-5a6b-4375-aeb0-8a6b394f5484logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Schachtelung von quantoren ([Beispiel]([[Beispiele]])):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;,323,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Vlogseq____&quot;,325,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Hlogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-623d-4a6c-a574-20f8c3c6e4a7logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]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;,329,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Vlogseq____&quot;,303,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Hlogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-8cf6-4772-a817-4c506ab94a57logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[311,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;,[311,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Flogseq____&quot;,331,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Vlogseq____&quot;,331,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,284,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Hlogseq____&quot;,284,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-3be3-4a1e-931e-1fe1c3fb7f7elogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[312,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;,[312,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Flogseq____&quot;,295,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Vlogseq____&quot;,295,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-c600-4ef4-884c-b6f38993306alogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Widerspruch = ↯, #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;,312,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Vlogseq____&quot;,312,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-b41d-4e53-bf72-ca23dacf730blogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Die beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der [[Aussagenlogik]]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;,302,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Vlogseq____&quot;,303,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,274,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,293,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Hlogseq____&quot;,274,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Hlogseq____&quot;,293,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-1876-4843-9073-2b67083fab7dlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]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;,323,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Vlogseq____&quot;,323,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,273,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,285,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,290,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Hlogseq____&quot;,273,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Hlogseq____&quot;,285,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Hlogseq____&quot;,290,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-e521-4927-9456-a823e5cb3c14logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist wahr}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Flogseq____&quot;,304,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Vlogseq____&quot;,304,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ulogseq____&quot;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Hlogseq____&quot;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-22a8-4da5-be6d-a3023244e00elogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[317,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;,[317,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Flogseq____&quot;,302,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Vlogseq____&quot;,302,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Ulogseq____&quot;,226,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Ulogseq____&quot;,234,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Hlogseq____&quot;,226,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Hlogseq____&quot;,234,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-be54-4822-adfc-9ffebdadf640logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x,y)$ AF in Variablen $x,y$ über $U_1,U_2$\\n\\\\begin{align}\\n\\\\underbrace{\\\\forall x: \\\\underbrace{\\\\exists y: p(x,y)}_{\\\\text{AF in den Variablen }x\\\\text{ über }U_1}}_{\\\\text{Aussage}}\\n\\\\end{align}logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Flogseq____&quot;,309,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Vlogseq____&quot;,309,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-96cc-4d0b-a113-62f9283a9ad8logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Verschiedene [[Quantoren]] dürfen **nicht** vertauscht werdenlogseq____&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;,311,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Vlogseq____&quot;,331,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Hlogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-ce19-40bd-83db-2d8a4dec2ee3logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[320,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;,[320,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Flogseq____&quot;,314,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Vlogseq____&quot;,303,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-c0cf-405c-b571-6e5a401aadablogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[321,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;,[321,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Flogseq____&quot;,305,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Vlogseq____&quot;,305,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ulogseq____&quot;,272,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ulogseq____&quot;,275,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ulogseq____&quot;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Hlogseq____&quot;,272,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Hlogseq____&quot;,275,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-f5d5-494e-92fd-90fcb46af4d2logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Nach Ersetzung von $x$ in der AF $\\logseq____&quot;xlogseq____&lt;y\\logseq____&quot;$ durch eine konkrete Zahl entsteht eine AF in der Variablen $y$, z. Bsp. $\\logseq____&quot;17logseq____&lt;y\\logseq____&quot;$logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Flogseq____&quot;,297,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Vlogseq____&quot;,297,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-478a-4082-bbbc-eea7f00b03eelogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[323,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;,[323,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Flogseq____&quot;,325,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Vlogseq____&quot;,325,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ulogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-9de9-4441-ae89-2a469bd489d8logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])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;,326,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Vlogseq____&quot;,303,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Hlogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-2b2e-49bb-b67b-bace1f7a156clogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Regeln]]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;,308,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Vlogseq____&quot;,303,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ulogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,2],536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Jlogseq____&quot;,[],536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^Hlogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[325,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-97dc-4305-b3de-3bfaae10f22alogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Gleichartige]([[Gleichartig]]) [[Quantoren]] dürfen vertauscht werdenlogseq____&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;,325,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Vlogseq____&quot;,303,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Hlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^Hlogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[326,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-0cf6-434a-9b12-03a173b25a12logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Regeln]]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;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Vlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Ulogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Jlogseq____&quot;,[],536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^Hlogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^17logseq____&quot;,false,536870925]],[logseq____&quot;^15logseq____&quot;,[327,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531c82d-c396-430e-9ba7-0e6c857d5285logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[328,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche 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mit [[Variablen]] $x_1,\\\\cdots,x_n$, der bei Ersetzung jedes $x_j$ durch ein [Objekt]([[Objekt (Logik)]]) aus $U_j$ stets zu einer [Aussage]([[Aussagen]]) 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