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Lösung von } x^n-a=0 \\\\text{ ist } x=\\\\sqrt[n]a$ #FIXME ich glaube hier fehlt logseq____&gt;0 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$\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[43,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[43,logseq____&quot;^Flogseq____&quot;,63,536870918]],[logseq____&quot;^15logseq____&quot;,[43,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[43,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[43,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[43,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[43,logseq____&quot;^Hlogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[43,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[43,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-08d2-4fa1-8254-19af936674b1logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{array}{c} 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\\\\cdots\\\\end{array}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^Flogseq____&quot;,55,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-c316-4ae4-84b0-bb10bc894caalogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Potenzen]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^Flogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^Ulogseq____&quot;,23,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^Hlogseq____&quot;,23,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^17logseq____&quot;,false,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-8bfe-46ea-aa19-384d14ae598clogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{array}{c}\\n{0\\\\choose 0}\\n\\\\\\\\\\n{1\\\\choose 0} {1\\\\choose 1}\\n\\\\\\\\\\n{2\\\\choose 0} {2\\\\choose 1} {2\\\\choose 2}\\n\\\\\\\\\\n{3\\\\choose 0} {3\\\\choose 1} {3\\\\choose 2} {3\\\\choose 3}\\n\\\\\\\\\\n\\\\cdots\\n\\\\end{array}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Flogseq____&quot;,51,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-415d-483e-b8ff-79b272dcd4fdlogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn } 10^x=y \\\\text{, dann}$\\n\\\\begin{align}\\nxlogseq____&amp;=\\\\lg y logseq____&amp; ,r\\\\\\\\\\nxlogseq____&amp;=\\\\log_y10logseq____&amp;,f\\\\\\\\\\nxlogseq____&amp;=\\\\log_{10}ylogseq____&amp;,r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&amp;= \\\\ln 2 logseq____&amp;, r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&amp;= \\\\ln 8 logseq____&amp;, f \\\\\\\\\\n\\\\ln 4 + \\\\ln 2 logseq____&amp;= \\\\ln 8 logseq____&amp;, r \\\\\\\\\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Flogseq____&quot;,67,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-e1c0-4e12-8b43-3cf0d35f80f1logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[48,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;,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Flogseq____&quot;,56,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-fa6c-45a5-8c60-e0c957fc8b08logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Häufige Falle:}$\\n\\\\begin{align}\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&amp;=(-1)^\\\\frac22logseq____&amp;=(-1)^1logseq____&amp;=-1\\\\\\\\\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&amp;=1^\\\\frac12logseq____&amp;logseq____&amp;=1\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Flogseq____&quot;,57,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-02e4-42a4-950b-0e1167f4dbe4logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\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;,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Flogseq____&quot;,44,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-b56e-4e57-b451-8b297c007437logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Flogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,30,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Hlogseq____&quot;,30,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-f6a5-4176-88fa-9f339e36943clogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[52,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;,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Flogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-c82e-4109-9fad-6b5593220442logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Was ist Größer?logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Flogseq____&quot;,49,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-93a5-4efb-a170-f433a0eda341logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[54,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;,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Flogseq____&quot;,53,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-3f6d-41e0-8863-744c05cfb702logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Pascalsches Dreieck]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Flogseq____&quot;,48,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Hlogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-a2a5-4788-9384-c83a08e3ce92logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Allgemein}$\\n\\\\begin{align}\\n(a+b)^2logseq____&amp;=a^2+2ab+b^2logseq____&amp;,\\\\text{ 1. Binomische Formel}\\\\\\\\\\n(a-b)^2logseq____&amp;=a^2-2ab+b^2logseq____&amp;,\\\\text{ 2. Binomische Formel}\\\\\\\\\\n(a+b)(a-b)logseq____&amp;=a^2-b^2logseq____&amp;,\\\\text{ 3. Binomische Formel}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Flogseq____&quot;,61,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-eb10-4ca0-a8ac-7f690c47e86flogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn }alogseq____&gt;0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=a\\\\sqrt{a}logseq____&amp;,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=a^2-\\\\sqrt{a}logseq____&amp;,f\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=\\\\sqrt{a^3}logseq____&amp;,r\\\\\\\\\\n\\\\frac{a^2}{\\\\sqrt{a}}logseq____&amp;=a^{\\\\frac32}logseq____&amp;,r\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Flogseq____&quot;,58,536870918]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-4a1a-4368-aaf8-d80963230586logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Wurzeln]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Flogseq____&quot;,37,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,29,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Hlogseq____&quot;,29,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-11b6-4648-8028-20088f5a4b01logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;![draws/2023-10-08-21-23-31.excalidraw](../assets/excalidraw_svg/2023-10-08-21-23-31.svg)logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Flogseq____&quot;,65,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-a6dc-4fec-b8e1-526de7ec4872logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 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logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870918]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Hlogseq____&quot;,28,536870918]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-273d-4032-af55-ca3bf7e7bea3logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Binomische Formeln]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Flogseq____&quot;,43,536870918]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,27,536870918]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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Falschlogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Flogseq____&quot;,50,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Hlogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-d548-49a0-b95b-674faa6ef851logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche 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[[Potenzen]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Flogseq____&quot;,46,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,23,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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\\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=e^x*e^ylogseq____&amp;,f\\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=ln(e^x+y)logseq____&amp;,x+ylogseq____&gt;0\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Flogseq____&quot;,45,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-9caf-4894-85e6-21b6dd8dd717logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____&gt;0$ welche keinen Sinn 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Wissensabgleich [[Logarithmen]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Flogseq____&quot;,59,536870918]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Xlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Vlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Ulogseq____&quot;,25,536870918]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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Bestimmung des }$[[Wahrheitswerteverlauf]]$\\\\text{ von }(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)$\\n|$p$|$q$||$p\\\\rightarrow q$|$q\\\\rightarrow p$|$(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)|$p\\\\leftrightarrow 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Beispiel}$\\n\\\\begin{align}\\n(p\\\\rightarrow q)logseq____&amp;\\\\equiv((\\\\neg q)\\\\rightarrow(\\\\neg p))\\\\\\\\\\n(p\\\\land(p\\\\rightarrow q)) logseq____&amp;\\\\rightarrow q logseq____&amp;\\\\quad \\\\text{Tantologie}\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Flogseq____&quot;,112,536870920]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Xlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Vlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^Ulogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[97,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-add2-4ea2-9999-05f4e2fe878clogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Satz, der wahr oder falsch ist, d.h. der [[Wahrheitswert]] $w$ bzw $f$ hat ($t/f$, $1/0$, $\\\\text{wahr}/\\\\text{falsch}$)logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Flogseq____&quot;,108,536870920]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Xlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Vlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Ulogseq____&quot;,80,536870920]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Ulogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^Hlogseq____&quot;,80,536870920]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[98,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-b8f5-4d1c-8db2-bd8273fdfdbclogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Verknüpfung von Aussagen]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Flogseq____&quot;,113,536870920]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Xlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Vlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Ulogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Ulogseq____&quot;,93,536870920]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870920]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Jlogseq____&quot;,[],536870920]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^Hlogseq____&quot;,93,536870920]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[99,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-dbeb-4f62-8f40-102adf948870logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Aussagenlogische variable]]: [[Variable]], die den Wert $w$ oder $f$ annimmtlogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Flogseq____&quot;,110,536870920]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Xlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Vlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Ulogseq____&quot;,77,536870920]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Ulogseq____&quot;,86,536870920]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Ulogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Hlogseq____&quot;,77,536870920]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^Hlogseq____&quot;,86,536870920]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[100,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-72f1-4f3c-b829-62a19afc6113logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[101,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;C. Meinel, M. Mundhenk, [[\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. Auflage 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Büchertiplogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Flogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Xlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Vlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Ulogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870920]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^Jlogseq____&quot;,[],536870920]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^17logseq____&quot;,false,536870920]],[logseq____&quot;^15logseq____&quot;,[102,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-8907-45f6-b251-af401663d530logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\np\\\\land q\\\\lor r\\\\\\\\\\n(p\\\\land q)\\\\lor r\\\\\\\\\\np\\\\land (q\\\\lor r)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Flogseq____&quot;,106,536870920]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Xlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Vlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^Ulogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[103,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-dc6e-4195-889b-b6a81c593a99logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[104,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Kontradiktion]]: Formel, die konstant $f$ 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[[Wahrheitswert]] der [[Formel]] zugeordnet (nach 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1. [[Aussagen]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Flogseq____&quot;,105,536870920]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Xlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Vlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Ulogseq____&quot;,88,536870920]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Ulogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870920]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Jlogseq____&quot;,[],536870920]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^Hlogseq____&quot;,88,536870920]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[108,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-1c72-4ffa-9518-fb97c83d3edalogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Flogseq____&quot;,97,536870920]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Xlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Vlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^Ulogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[109,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-226a-46fd-9021-a994e7c62c0blogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Soweit die \\logseq____&quot;[[Syntax]]\\logseq____&quot;, jetzt die [[Semantik]]. Die [[Wahrheitswert]]e\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Flogseq____&quot;,103,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Xlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Vlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ulogseq____&quot;,80,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ulogseq____&quot;,84,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ulogseq____&quot;,87,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ulogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Ulogseq____&quot;,92,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Hlogseq____&quot;,80,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Hlogseq____&quot;,84,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Hlogseq____&quot;,87,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^Hlogseq____&quot;,92,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[110,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-2761-4036-9070-811a4583e051logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Belegung]] (der Variablen): Zuordnung von $w/f$ an jede [[Variable]] einer [[Aussageformel]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Flogseq____&quot;,115,536870920]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Xlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Vlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Ulogseq____&quot;,86,536870920]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Ulogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Ulogseq____&quot;,91,536870920]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Ulogseq____&quot;,95,536870920]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Hlogseq____&quot;,86,536870920]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Hlogseq____&quot;,91,536870920]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^Hlogseq____&quot;,95,536870920]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[111,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-ce0c-4a8b-b6d3-f273fcf60baelogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Flogseq____&quot;,116,536870920]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Xlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Vlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Ulogseq____&quot;,82,536870920]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Ulogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^Hlogseq____&quot;,82,536870920]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[112,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-a9eb-4f94-a14a-24670c643614logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\n\\logseq____&quot;5\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;\\\\quadlogseq____&amp; (w)\\\\\\\\\\n\\logseq____&quot;4\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;logseq____&amp; (f)\\\\\\\\\\n\\logseq____&quot;\\\\text{Jede gerade Zahl }\\\\ge4\\\\notag\\\\\\\\\\n\\\\text{ ist Summe zweier Primzahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage, }w\\\\text{ oder }f)\\\\\\\\\\n(\\\\text{Vermutung von Goldback 1742})\\\\text{, }logseq____&amp;logseq____&amp;\\\\text{richtig für gerade Zahlen bis }4*10^{18}\\\\notag\\\\\\\\\\n\\logseq____&quot;\\\\text{Dieser Satz ist falsch}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{keine Aussage})\\\\\\\\\\n\\logseq____&quot;\\\\text{Die Gleichung } x^2+y^2=z^2 \\\\notag\\\\\\\\\\n\\\\text{ hat eine Lösung }x,y,z\\\\notag\\n\\\\\\\\\\\\text{ aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\logseq____&quot;\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nx^n+y^n=z^n\\\\text{ eine Lösung}logseq____&amp;logseq____&amp; (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nx,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp;\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\logseq____&quot;\\\\text{Gott ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\logseq____&quot;\\\\text{Nietzsche ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage?}) \\\\\\\\\\n\\logseq____&quot;\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\n\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\n\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\n\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Flogseq____&quot;,98,536870920]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Xlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Vlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^Ulogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[113,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-28fe-46ec-9abd-7e46d3d6ded5logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Tantologie]]: Formel, die konstant $w$ istlogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^Flogseq____&quot;,96,536870920]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^Xlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^Vlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^Ulogseq____&quot;,82,536870920]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^Ulogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^Hlogseq____&quot;,82,536870920]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[114,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-6224-4e74-86e5-faf8e453e535logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Aussageformel]]: Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Flogseq____&quot;,100,536870920]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Xlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Vlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Ulogseq____&quot;,32,536870920]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Ulogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Ulogseq____&quot;,90,536870920]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Ulogseq____&quot;,91,536870920]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Hlogseq____&quot;,32,536870920]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Hlogseq____&quot;,90,536870920]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^Hlogseq____&quot;,91,536870920]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[115,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-1839-4a3d-a870-0061906c5755logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formeln $p,q$ [[logisch äquivalent]], wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Flogseq____&quot;,104,536870920]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Xlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Vlogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Ulogseq____&quot;,76,536870920]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Ulogseq____&quot;,85,536870920]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Ulogseq____&quot;,89,536870920]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Ulogseq____&quot;,94,536870920]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Hlogseq____&quot;,76,536870920]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Hlogseq____&quot;,85,536870920]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^Hlogseq____&quot;,94,536870920]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[116,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251170-db3b-4272-994e-c11434b31012logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Klogseq____&quot;,1696928113083,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^@logseq____&quot;,false,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;logarithmusgesetzelogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^11logseq____&quot;,logseq____&quot;Logarithmusgesetzelogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^Blogseq____&quot;,1696928113083,536870921]],[logseq____&quot;^15logseq____&quot;,[118,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251171-6c53-467b-9321-6aceb8aea902logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Logarithmusgesetze]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Flogseq____&quot;,25,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Xlogseq____&quot;,25,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Vlogseq____&quot;,25,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Ulogseq____&quot;,25,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Ulogseq____&quot;,118,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Hlogseq____&quot;,118,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251171-fe2e-4bba-9db9-2c708380e49dlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Flogseq____&quot;,119,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Xlogseq____&quot;,25,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Vlogseq____&quot;,25,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Ulogseq____&quot;,25,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65251171-328c-4902-82e1-e74c1ccf102flogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Klogseq____&quot;,1696928113130,536870924]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^@logseq____&quot;,false,536870924]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;vorlesungs 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