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[[Rationalmachen]] des [[Nenner]]slogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Flogseq____&quot;,89,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Vlogseq____&quot;,81,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,72,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,78,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,2],536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Hlogseq____&quot;,72,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Hlogseq____&quot;,78,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-4113-40a7-aef1-bcea3d98281elogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel]([[Beispiele]])logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Flogseq____&quot;,115,536870921]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Vlogseq____&quot;,115,536870921]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,62,536870921]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,74,536870921]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,76,536870921]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Hlogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-cc8c-40b2-8489-a2bbbf104710logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Allgemein}$\\n\\\\begin{align}\\n|y|logseq____&amp;=\\\\begin{cases}\\ny logseq____&amp;\\\\text{ falls } y\\\\ge0\\\\\\\\\\n-y logseq____&amp;\\\\text{ falls } ylogseq____&lt;0\\\\\\\\\\n\\\\end{cases}\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Flogseq____&quot;,131,536870921]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Vlogseq____&quot;,81,536870921]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[89,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-bf9b-4404-822c-e2dbfc4365f3logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Für } x=\\\\frac25 \\\\text{ und } y=\\\\frac37 \\\\text{ ist }\\\\frac xy$\\n\\\\begin{align}\\n\\\\frac xy = \\\\frac{\\\\frac25}{\\\\frac37} = \\\\frac{2*7}{3*5}=\\\\frac{14}{15}\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Flogseq____&quot;,93,536870921]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Vlogseq____&quot;,93,536870921]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[90,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-0524-4252-9aae-98932f1615a7logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Logarithmen]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Flogseq____&quot;,119,536870921]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Vlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,64,536870921]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^Hlogseq____&quot;,64,536870921]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[91,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-026d-4203-ac0e-4e91364f4499logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[92,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;,[92,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Flogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Vlogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-11ff-440d-a53a-3c8144eb18e6logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Was ist Größer?logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Flogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Vlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-d189-46dd-a8eb-469e532ed9e3logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[94,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;,[94,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Flogseq____&quot;,99,536870921]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Vlogseq____&quot;,99,536870921]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,72,536870921]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Ulogseq____&quot;,78,536870921]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-948a-4063-b75a-ef5686b95769logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[95,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 x)^5*(1-\\\\sqrt x)^5logseq____&amp;=2+20x+40x^2\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Flogseq____&quot;,113,536870921]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Vlogseq____&quot;,113,536870921]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,61,536870921]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[95,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-516d-4319-b774-801c012d7678logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\sqrt[n]{a^n}logseq____&amp;=1^\\\\frac nn=a^1=a\\\\\\\\\\n\\\\sqrt[n]{\\\\frac ab} logseq____&amp;= \\\\frac{\\\\sqrt[n]a}{\\\\sqrt[n]b}\\\\\\\\\\n\\\\left(\\\\sqrt[n]a\\\\right)^mlogseq____&amp;=a^\\\\frac mn\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Flogseq____&quot;,98,536870921]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Vlogseq____&quot;,81,536870921]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[96,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[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;~u6531cce1-9bf9-4bc3-bf2e-ac28906eb8f7logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Herleitung mit }$[[Quadratische Ergänzung]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&amp;=0logseq____&amp;|logseq____&amp;-q\\\\\\\\\\nx^2+pxlogseq____&amp;=-qlogseq____&amp;|logseq____&amp;+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\nx^2+px+\\\\left(\\\\frac p2\\\\right)^2logseq____&amp;=-q+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\n\\\\underbrace{\\\\left(x+\\\\frac p2\\\\right)^2}_\\\\text{1. binomische Formel}logseq____&amp;=-q+\\\\left(\\\\frac p2\\\\right)^2logseq____&amp;|logseq____&amp;\\\\sqrt{()}\\\\\\\\\\n\\\\left|x+\\\\frac p2\\\\right|logseq____&amp;=\\\\sqrt{\\\\frac{p^2}4-q}logseq____&amp;,logseq____&amp;\\\\text{ falls }\\\\frac{p^2}4-q\\\\ge0\\\\\\\\\\nx+\\\\frac p2logseq____&amp;=\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}logseq____&amp;|logseq____&amp;-\\\\frac p2\\\\\\\\\\nxlogseq____&amp;=-\\\\frac p2\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Flogseq____&quot;,137,536870921]],[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;,59,536870921]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Ulogseq____&quot;,62,536870921]],[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;^Ulogseq____&quot;,76,536870921]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Hlogseq____&quot;,59,536870921]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-53bb-4979-8114-79a32a2e1669logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[98,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;,[98,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Flogseq____&quot;,81,536870921]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Vlogseq____&quot;,81,536870921]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[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;^Ulogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Hlogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-e591-49f4-a64a-a78fb6f579a1logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Flogseq____&quot;,124,536870921]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Vlogseq____&quot;,87,536870921]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Ulogseq____&quot;,72,536870921]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Ulogseq____&quot;,78,536870921]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Hlogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-6031-4093-8891-8b68193c0d96logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;![draws/2023-10-08-21-23-31.excalidraw](https://raw.githubusercontent.com/Surferlul/IA-Logseq-Publish/external-assets/svg-assets/draws/2023-10-08-21-23-31.excalidraw.svg)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;,80,536870921]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Vlogseq____&quot;,119,536870921]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[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;~u6531cce1-5cdf-40a3-b9f3-1073f306b125logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel für die 3. Binomische Formel}$\\n\\\\begin{align}\\n\\\\frac{\\\\frac1{a-b}+\\\\frac1{a+b}}{\\\\frac1{a-b}-\\\\frac1{a+b}}\\nlogseq____&amp;=\\\\frac{\\\\frac{a+b+a-b}{(a+b)*(a-b)}}{\\\\frac{a+b-(a-b)}{(a+b)*(a-b)}}\\nlogseq____&amp;=\\\\frac{a+b+a-b}{a+b-a+b}\\nlogseq____&amp;=\\\\frac{2a}{2b}\\nlogseq____&amp;=\\\\frac ab\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Flogseq____&quot;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Vlogseq____&quot;,136,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-38c9-4d79-a083-220abb990ee2logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Wurzelgleichung]]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;,126,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Vlogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Ulogseq____&quot;,63,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Hlogseq____&quot;,63,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-ef67-49c1-8f64-7e86770de20clogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[103,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;,[103,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Flogseq____&quot;,126,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Vlogseq____&quot;,126,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Ulogseq____&quot;,62,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-d9c4-47d1-b7b1-a60da45e3790logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____&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;,82,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^Vlogseq____&quot;,82,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^Ulogseq____&quot;,69,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^Ulogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^Hlogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-d27c-49f7-8ba9-3c0a454d05eflogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[105,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;,[105,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^Flogseq____&quot;,131,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^Vlogseq____&quot;,131,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[105,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-0eb0-4d55-a4b9-7e515a2866a5logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche quadratische Gleichung hat die Lösung}$\\n$x_1=3\\\\quad x_2=4$\\n\\\\begin{align}\\nx_1+x_2 = 7 logseq____&amp;= p logseq____&amp;, x_1x_2=12=q\\\\\\\\\\nx^2+px+qlogseq____&amp;=0\\\\\\\\\\nx^2-7x+12logseq____&amp;=0\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Flogseq____&quot;,88,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Vlogseq____&quot;,88,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Ulogseq____&quot;,62,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Ulogseq____&quot;,74,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^Ulogseq____&quot;,76,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[106,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-b9e6-4901-bd67-dad16968deadlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[107,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;,[107,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^Flogseq____&quot;,105,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^Vlogseq____&quot;,131,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^Ulogseq____&quot;,60,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^Ulogseq____&quot;,68,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^Ulogseq____&quot;,70,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^Ulogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^Hlogseq____&quot;,75,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[107,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-9eee-457d-b305-21453af89cdalogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wolframalpha]]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;,135,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Vlogseq____&quot;,135,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Ulogseq____&quot;,77,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Ulogseq____&quot;,79,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Hlogseq____&quot;,79,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-7007-4b90-ab0a-73baa482076flogseq____&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;,91,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Vlogseq____&quot;,91,536870921]],[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;~u6531cce1-a7d7-4469-b881-7ec1ea8d8569logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Alte Schreibweise}$\\n\\\\begin{align}\\n\\\\text{cosa }logseq____&amp;\\\\text{plus }logseq____&amp;\\\\text{cubus }logseq____&amp;\\\\text{acq 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von Vieta]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&amp;=0 logseq____&amp;logseq____&amp; \\\\text{habe }x_{1,2}\\\\text{ als Lösung}\\\\\\\\\\nx_1+x_2logseq____&amp;=-p logseq____&amp;logseq____&amp; 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[[Pascalsches Dreieck]]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;,101,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Xlogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Vlogseq____&quot;,136,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,61,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,67,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,73,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten 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aller reellen Zahlen zwischen 1 und 4 inklusive 1 und 4\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-1\\\\le x\\\\le4\\\\right\\\\}=:\\\\underbrace{[-1,4]}_\\\\text{Abgeschlossenes 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Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Flogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Xlogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Vlogseq____&quot;,182,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,68,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Ulogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^Hlogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[180,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-55bd-4544-a464-de40ed6bc0f0logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[181,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Menge]([[Mengen]]) von [Punkten]([[Punkte]]) $(x,y)$ in der [Ebene]([[Ebenen]]) die den gleichen [[Abstand]] r ([[Radius]]) zu einem [festen Punkt]([[Fester Punkt]]) 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[[Betragsungleichungen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Flogseq____&quot;,216,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Xlogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Vlogseq____&quot;,199,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,158,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Hlogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-e72b-4b7e-a39e-fd82ec8f7395logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;**oder** $\\\\rightarrow$ 5 ist abstand von x zu 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an [Punkten]([[Punkte]]) $(x,y)$ der [Ebene]([[Ebenen]]) bei denen die [[Summe]] der [Abstände]([[Abstand]]) der Punkte zu zwei [festen Punkten]([[Fester Punkt]]) $F_1,F_2$ ([Brennpunkte]([[Brennpunkt]])) [[konstant]] 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Lösung mit 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2011logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[227,logseq____&quot;^Blogseq____&quot;,1697762529692,536870924]],[logseq____&quot;^15logseq____&quot;,[227,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-f635-477f-a10a-fc1fc0ee5aablogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[228,logseq____&quot;^Klogseq____&quot;,1697762529706,536870924]],[logseq____&quot;^15logseq____&quot;,[228,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[228,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;tantologielogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[228,logseq____&quot;^11logseq____&quot;,logseq____&quot;Tantologielogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[228,logseq____&quot;^Blogseq____&quot;,1697762529706,536870924]],[logseq____&quot;^15logseq____&quot;,[228,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-0034-408d-a263-a7dd4ab1ed7elogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^Klogseq____&quot;,1697762529704,536870924]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;kontradiktionlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^11logseq____&quot;,logseq____&quot;Kontradiktionlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^Blogseq____&quot;,1697762529704,536870924]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-37a4-4663-8a9e-325b9390a29clogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Klogseq____&quot;,1697762529701,536870924]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;variablenlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^11logseq____&quot;,logseq____&quot;Variablenlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Blogseq____&quot;,1697762529701,536870924]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-0452-441d-9b75-f217a00bd801logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^Klogseq____&quot;,1697762529697,536870924]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;semantiklogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^11logseq____&quot;,logseq____&quot;Semantiklogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^Blogseq____&quot;,1697762529697,536870924]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-e8a4-46a1-9007-e3cba76a7f97logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Klogseq____&quot;,1697762529706,536870924]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;logisch äquivalentlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^11logseq____&quot;,logseq____&quot;Logisch Äquivalentlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Blogseq____&quot;,1697762529706,536870924]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-c962-459b-8b94-8e7259f3dfbblogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Klogseq____&quot;,1697762529702,536870924]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;tabellenregelnlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^11logseq____&quot;,logseq____&quot;Tabellenregelnlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Blogseq____&quot;,1697762529702,536870924]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-94b0-46fe-807d-b11666ebadb5logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Klogseq____&quot;,1697762529695,536870924]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;aussagenlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^11logseq____&quot;,logseq____&quot;Aussagenlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Blogseq____&quot;,1697762529695,536870924]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-3978-4053-83f8-2c223baf4629logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Klogseq____&quot;,1697762529700,536870924]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;verknüpfungenlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^11logseq____&quot;,logseq____&quot;Verknüpfungenlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Blogseq____&quot;,1697762529700,536870924]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-471b-4854-a14b-ee5b45233559logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Klogseq____&quot;,1697762529701,536870924]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;aussageformellogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^11logseq____&quot;,logseq____&quot;Aussageformellogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Blogseq____&quot;,1697762529701,536870924]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-3fbb-48d1-9627-d641fd5d4599logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Klogseq____&quot;,1697762529697,536870924]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;syntaxlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^11logseq____&quot;,logseq____&quot;Syntaxlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Blogseq____&quot;,1697762529697,536870924]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-e7b8-4951-bb35-83aafe79c915logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Klogseq____&quot;,1697762529695,536870924]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;verknüpfung von aussagenlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^11logseq____&quot;,logseq____&quot;Verknüpfung von Aussagenlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Blogseq____&quot;,1697762529695,536870924]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-c6d7-4a64-8cef-2a63793ec2e7logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Klogseq____&quot;,1697762529705,536870924]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;schreibweiselogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^11logseq____&quot;,logseq____&quot;Schreibweiselogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Blogseq____&quot;,1697762529705,536870924]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-f7fd-4657-9ffd-45355427d209logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Klogseq____&quot;,1697762529703,536870924]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;belegunglogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^11logseq____&quot;,logseq____&quot;Belegunglogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^Blogseq____&quot;,1697762529703,536870924]],[logseq____&quot;^15logseq____&quot;,[240,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-79f8-4f5c-9cca-b8ca3198d201logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[241,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;,[241,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Flogseq____&quot;,256,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Vlogseq____&quot;,250,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,226,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,231,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,233,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,237,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Hlogseq____&quot;,226,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Hlogseq____&quot;,231,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Hlogseq____&quot;,233,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^Hlogseq____&quot;,237,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[241,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-3091-48ae-b941-d64fbe9b2af7logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[242,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;,[242,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Flogseq____&quot;,261,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Vlogseq____&quot;,250,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,222,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,232,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Ulogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Hlogseq____&quot;,222,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Hlogseq____&quot;,232,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^Hlogseq____&quot;,239,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[242,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-d3cd-47bb-a6a0-9ba20f3d5cbelogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[243,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;,[243,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Flogseq____&quot;,257,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Vlogseq____&quot;,248,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[243,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-415c-48ba-9826-5fd77680e8c1logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $w$ istlogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Flogseq____&quot;,249,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Vlogseq____&quot;,249,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,228,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[244,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-151a-447c-9d70-45b6180750a9logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Büchertiplogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Flogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Vlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^17logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[245,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-b0e1-44f6-b835-973c77ae1733logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\np\\\\land q\\\\lor r\\\\\\\\\\n(p\\\\land q)\\\\lor r\\\\\\\\\\np\\\\land (q\\\\lor r)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Flogseq____&quot;,256,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Vlogseq____&quot;,256,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,68,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[246,logseq____&quot;^Ulogseq____&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;~u6531cce1-c5c4-4b11-a43c-1649abfd20belogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussagenlogische Variable]]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;,241,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Vlogseq____&quot;,250,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,223,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^Hlogseq____&quot;,223,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[247,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-38cd-4710-9334-4dfe82366420logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 1. [[Aussagen]]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;,245,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Vlogseq____&quot;,219,536870924]],[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;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^Hlogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[248,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-9c24-417e-942e-56805d725085logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Tantologie]]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;,254,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Vlogseq____&quot;,250,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Ulogseq____&quot;,228,536870924]],[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;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^Hlogseq____&quot;,228,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[249,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-d16b-4992-9591-44de489e2906logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Verknüpfung von Aussagen]]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;,243,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Vlogseq____&quot;,248,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,2],536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^Hlogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[250,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-e2a2-4698-b481-626c8fb14477logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Flogseq____&quot;,262,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Vlogseq____&quot;,262,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,75,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Hlogseq____&quot;,75,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^Hlogseq____&quot;,235,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[251,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-f63e-498e-898e-1f5e35067db4logseq____&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;,250,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[252,logseq____&quot;^Vlogseq____&quot;,250,536870924]],[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;~u6531cce1-5c8b-4209-8444-56f617b55c37logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])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;,254,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Vlogseq____&quot;,254,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,222,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,225,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,226,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,233,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Ulogseq____&quot;,240,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Hlogseq____&quot;,225,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Hlogseq____&quot;,226,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Hlogseq____&quot;,233,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^Hlogseq____&quot;,240,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[253,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-c257-477d-8833-f1b0356dacf6logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Flogseq____&quot;,259,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Vlogseq____&quot;,250,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,222,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,3],536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Jlogseq____&quot;,[],536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Hlogseq____&quot;,222,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^Hlogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[254,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-2734-46e0-a49b-b421eb4ea0a0logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $f$ istlogseq____&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;,261,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Vlogseq____&quot;,261,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,229,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[255,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-ddde-4b3d-8887-0df240c7f088logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Flogseq____&quot;,252,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Vlogseq____&quot;,250,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,68,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,234,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^Hlogseq____&quot;,68,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[256,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-f990-4649-9fbf-8a339f22d407logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[257,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Satz, der wahr oder falsch ist, d.h. der [[Wahrheitswert]] $w$ bzw $f$ hat ($t/f$, $1/0$, 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[[Aussageformel]]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;,247,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Vlogseq____&quot;,250,536870924]],[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;^Ulogseq____&quot;,236,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^Ulogseq____&quot;,238,536870924]],[logseq____&quot;^15logseq____&quot;,[262,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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von $w/f$ an jede [Variable]([[Variablen]]) 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;,259,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Vlogseq____&quot;,259,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Ulogseq____&quot;,230,536870924]],[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;^Ulogseq____&quot;,240,536870924]],[logseq____&quot;^15logseq____&quot;,[265,logseq____&quot;^Hlogseq____&quot;,230,536870924]],[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;~u6531cce1-dfea-4530-bade-8fdd0b1886e4logseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wikipedia]]logseq____&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;,264,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Xlogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Vlogseq____&quot;,245,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,219,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Ulogseq____&quot;,224,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^Hlogseq____&quot;,224,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^17logseq____&quot;,true,536870924]],[logseq____&quot;^15logseq____&quot;,[266,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-d96f-483d-b862-749e3f0af03flogseq____&quot;,536870924]],[logseq____&quot;^15logseq____&quot;,[267,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Variable]([[Variablen]]), 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(Logik)logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^Blogseq____&quot;,1697762529875,536870925]],[logseq____&quot;^15logseq____&quot;,[292,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-d335-4ce7-8c9d-80cfe26f2aa7logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Klogseq____&quot;,1697762529880,536870925]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^@logseq____&quot;,false,536870925]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;sprachenlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^11logseq____&quot;,logseq____&quot;Sprachenlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^Blogseq____&quot;,1697762529880,536870925]],[logseq____&quot;^15logseq____&quot;,[293,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-3fdf-453b-a11b-b8fdc573e78alogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Klogseq____&quot;,1697762529877,536870925]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^@logseq____&quot;,false,536870925]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;objekt (logik)logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^11logseq____&quot;,logseq____&quot;Objekt (Logik)logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^Blogseq____&quot;,1697762529877,536870925]],[logseq____&quot;^15logseq____&quot;,[294,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-777c-4fca-86ee-42c2e60766c5logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Allquantor]] [[Existenzquantor]]logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Flogseq____&quot;,307,536870925]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Vlogseq____&quot;,307,536870925]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Ulogseq____&quot;,283,536870925]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Ulogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Hlogseq____&quot;,283,536870925]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^Hlogseq____&quot;,289,536870925]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[295,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-7ad6-4dd2-a7d2-6320e58e3136logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXMElogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Flogseq____&quot;,315,536870925]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Vlogseq____&quot;,315,536870925]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Ulogseq____&quot;,75,536870925]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^Hlogseq____&quot;,75,536870925]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[296,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-22be-4b57-b448-c678282e4850logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Gleichartige]([[Gleichartig]]) [[Quantoren]] dürfen vertauscht werdenlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Flogseq____&quot;,310,536870925]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Vlogseq____&quot;,324,536870925]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Hlogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^Hlogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[297,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-503e-4425-a37f-ef1c9cea09a9logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[298,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;,[298,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Flogseq____&quot;,321,536870925]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Vlogseq____&quot;,321,536870925]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[298,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-d9dc-4f2a-bcb6-f7f16460bd2blogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[299,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;,[299,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Flogseq____&quot;,310,536870925]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Vlogseq____&quot;,310,536870925]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Ulogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[299,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-6072-4b51-9485-3f810c9671cdlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[300,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;,[300,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Flogseq____&quot;,323,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Vlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[300,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-8dce-4801-8fab-3d21493b41f1logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x)$ AF in der Variablen $x$ über $U$:logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Flogseq____&quot;,321,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Vlogseq____&quot;,324,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[301,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-7517-423e-80d2-07559daac4b3logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]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;,299,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Vlogseq____&quot;,299,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,273,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,285,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Ulogseq____&quot;,290,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Hlogseq____&quot;,273,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Hlogseq____&quot;,285,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^Hlogseq____&quot;,290,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[302,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-2c76-46bc-9ba8-91ce32c95aaalogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nlogseq____&amp;\\\\neg\\\\left(\\\\forall x :\\\\exists y :\\\\forall w :\\\\forall u :\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)\\\\right)\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x:(\\\\neg(\\\\exists y: \\\\forall w: \\\\forall u: \\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x:\\\\forall y:(\\\\neg(\\\\forall w: \\\\forall u:\\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x:\\\\forall y:\\\\exists w:(\\\\neg(\\\\forall u:\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&amp;\\\\exists x: \\\\forall y: \\\\exists w: \\\\exists u : \\\\forall z:\\\\neg(p(x,y,z)\\\\rightarrow q(u,w))\\n\\\\end{align}logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Flogseq____&quot;,326,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Vlogseq____&quot;,326,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[303,logseq____&quot;^Ulogseq____&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;~u6531cce1-c7aa-4d51-9932-4894fcdd64b6logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Widerspruch = ↯, #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;,325,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[304,logseq____&quot;^Vlogseq____&quot;,325,536870925]],[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;,281,536870925]],[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;~u6531cce1-8345-4883-97cc-e621dc7d3d28logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]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;,313,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Vlogseq____&quot;,324,536870925]],[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;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^Hlogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[305,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-cd85-4969-b577-83c503880b7dlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[306,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;,[306,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Flogseq____&quot;,329,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Vlogseq____&quot;,329,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,284,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^Hlogseq____&quot;,284,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[306,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-c5b2-4dc1-b1d3-41700085ec4elogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\underbrace{\\\\forall}_\\\\text{Allquantor} x: p(x) logseq____&amp;\\\\equiv p(O_1) \\\\land p(O_2) \\\\land \\\\cdots \\\\land p(O_m)\\\\\\\\\\n\\\\underbrace{\\\\exists}_\\\\text{Existenzquantor} x: p(x) logseq____&amp;\\\\equiv p(0_1) \\\\lor p(O_2) \\\\lor \\\\cdots \\\\lor p(0_m)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Flogseq____&quot;,320,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Vlogseq____&quot;,324,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[307,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-9885-4d81-a14d-908ccbd25f34logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[308,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;,[308,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Flogseq____&quot;,330,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Vlogseq____&quot;,330,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[308,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[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;~u6531cce1-85dc-4ae1-8ddd-544d2f248c10logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[309,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;,[309,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Flogseq____&quot;,318,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Vlogseq____&quot;,318,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[309,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-297f-4fa6-af8f-7db5386878a9logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Regeln]]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;,315,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Vlogseq____&quot;,324,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Ulogseq____&quot;,270,536870925]],[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;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,2],536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Jlogseq____&quot;,[],536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^Hlogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[310,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-b193-4100-80b9-d468996039aflogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[311,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;,[311,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Flogseq____&quot;,309,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Vlogseq____&quot;,309,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,272,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,275,536870925]],[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;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Hlogseq____&quot;,272,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^Hlogseq____&quot;,275,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[311,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-1cf3-4336-9334-c11ff6a6575dlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Schachtelung von quantoren ([Beispiel]([[Beispiele]])):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;,299,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Vlogseq____&quot;,310,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^Hlogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[312,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-6bb3-4fee-92f1-ebb79ca237b3logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Satz]] mit [[Variablen]] $x_1,\\\\cdots,x_n$, der bei Ersetzung jedes $x_j$ durch ein [Objekt]([[Objekt (Logik)]]) aus $U_j$ stets zu einer [Aussage]([[Aussagen]]) wirdlogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Flogseq____&quot;,319,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Vlogseq____&quot;,324,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,230,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,234,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,291,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Ulogseq____&quot;,294,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Hlogseq____&quot;,230,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Hlogseq____&quot;,234,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Hlogseq____&quot;,291,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^Hlogseq____&quot;,294,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[313,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-c526-4c12-bbba-a01bd897a27blogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____&lt;y\\\\quad\\\\text{ist falsch}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Flogseq____&quot;,318,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Vlogseq____&quot;,308,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^Hlogseq____&quot;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[314,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-b109-4ce1-8b3c-5c9d69c14ca3logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[315,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;,[315,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Flogseq____&quot;,328,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Vlogseq____&quot;,324,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[315,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-d2d8-45ce-b658-f85e31e7fc12logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Die beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der [[Aussagenlogik]]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;,301,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Vlogseq____&quot;,324,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ulogseq____&quot;,274,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Ulogseq____&quot;,293,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Hlogseq____&quot;,274,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^Hlogseq____&quot;,293,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[316,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-4821-4c70-b459-3d06145b2caelogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[317,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;,[317,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Flogseq____&quot;,316,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^Vlogseq____&quot;,324,536870925]],[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;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[317,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-b2d1-455e-a12c-d9db003df6f2logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[318,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;,[318,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Flogseq____&quot;,308,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Vlogseq____&quot;,308,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,68,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,278,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,282,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^Hlogseq____&quot;,281,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[318,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-39f6-4d4b-a025-39eb892fc9c0logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Aussageform]] (AF) über [Universen]([[Universen (Logik)]]) $U_1,\\\\cdots,U_n$:logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Flogseq____&quot;,324,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Vlogseq____&quot;,324,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Ulogseq____&quot;,292,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Hlogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^Hlogseq____&quot;,292,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[319,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-f8b3-42c6-acbf-12b8fff128a6logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Endliches Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$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;,317,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[320,logseq____&quot;^Vlogseq____&quot;,324,536870925]],[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;~u6531cce1-5f7f-4641-99c5-1930fe5165c2logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\logseq____&quot;\\\\text{x ist prim}\\logseq____&quot; \\\\quad logseq____&amp; \\\\text{ist AF mit Variablen x über den natürlichen Zahlen}\\\\\\\\\\n\\logseq____&quot;\\\\underbrace{x}_{x_1}logseq____&lt;\\\\underbrace{y}_{x_2}\\logseq____&quot;\\\\quad logseq____&amp;\\\\text{ist AF mit Variablen }x,y\\\\text{ über die reellen Zahlen } \\\\underbrace{\\\\Reals}_{U_1},\\\\underbrace{\\\\Reals}_{U_2}\\\\\\\\\\n\\logseq____&quot;\\\\text{x ist wahr}\\logseq____&quot;\\\\quadlogseq____&amp;\\\\text{ist AF mit Variablen x über dem Universum der Aussagen}\\n\\\\end{align}logseq____&quot;,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;,324,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^Ulogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[321,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-205e-47f2-8a9b-1f89b6415555logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche Regeln]]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;,300,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Vlogseq____&quot;,300,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ulogseq____&quot;,271,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ulogseq____&quot;,276,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ulogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ulogseq____&quot;,279,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ulogseq____&quot;,280,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ulogseq____&quot;,286,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Ulogseq____&quot;,287,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Hlogseq____&quot;,271,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Hlogseq____&quot;,276,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Hlogseq____&quot;,279,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Hlogseq____&quot;,280,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Hlogseq____&quot;,286,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^Hlogseq____&quot;,287,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[322,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-a9d2-446e-ad76-6bc2093a076elogseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Regeln]]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;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Vlogseq____&quot;,277,536870925]],[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;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Jlogseq____&quot;,[],536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^Hlogseq____&quot;,270,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^17logseq____&quot;,false,536870925]],[logseq____&quot;^15logseq____&quot;,[323,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-687f-40d1-a9a1-9ce9e5db0434logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Aussageform]]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;,300,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Xlogseq____&quot;,277,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Vlogseq____&quot;,277,536870925]],[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;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^1Qlogseq____&quot;,1],536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Jlogseq____&quot;,[],536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^Hlogseq____&quot;,288,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^17logseq____&quot;,true,536870925]],[logseq____&quot;^15logseq____&quot;,[324,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u6531cce1-8a32-441f-987a-447a0a880cb7logseq____&quot;,536870925]],[logseq____&quot;^15logseq____&quot;,[325,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. 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