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logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870918]],[logseq____&quot;^15logseq____&quot;,[43,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[43,logseq____&quot;^Hlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[43,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[43,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-42ca-4396-b687-f0f48eccd852logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Wenn }alogseq____&gt;0\\\\text{, dann}$\\n\\\\begin{align}\\n\\\\frac b{\\\\sqrt a} = \\\\frac b{\\\\sqrt a}*\\\\frac{\\\\sqrt a}{\\\\sqrt a} = \\\\frac {b\\\\sqrt a}a\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^Flogseq____&quot;,56,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^Vlogseq____&quot;,56,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^Ulogseq____&quot;,34,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^Ulogseq____&quot;,38,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[44,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-49ea-42b7-9f65-a4ad58bafb66logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____&gt;0$ welche keinen Sinn ergibtlogseq____&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;,66,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^Vlogseq____&quot;,42,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^Hlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[45,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-1155-4659-9529-17697251e555logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[46,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;,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Flogseq____&quot;,42,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Vlogseq____&quot;,42,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^Hlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[46,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-cb08-4622-a018-bb85b26fe771logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\n\\\\tan x logseq____&amp;= \\\\frac{\\\\sin x}{\\\\cos x} logseq____&amp;, \\\\cos x \\\\ne 0\\\\\\\\\\n\\\\sin^{-2}x-\\\\cos^2xlogseq____&amp;=1logseq____&amp;,f\\\\\\\\\\n\\\\sin x = \\\\cos x logseq____&amp;= 1 logseq____&amp;, f\\\\\\\\\\n\\\\sin^{-2}x+cos^2ylogseq____&amp;=1logseq____&amp;,r\\\\\\\\\\n1+tan^2xlogseq____&amp;=\\\\frac1{\\\\cos^2x}logseq____&amp;,\\\\cos x\\\\ne0\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Flogseq____&quot;,62,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Vlogseq____&quot;,43,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[47,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-02ea-4fc6-9368-1216f7d7f8c8logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[48,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;,[48,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Flogseq____&quot;,59,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Vlogseq____&quot;,40,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Ulogseq____&quot;,25,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Ulogseq____&quot;,28,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Ulogseq____&quot;,30,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-be57-4e23-b587-244f1b0b74c6logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____&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;,43,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Vlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Hlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-dba6-445c-80a8-7eec6df99f1dlogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[50,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;,[50,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Flogseq____&quot;,81,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Vlogseq____&quot;,81,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,27,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-f101-4146-a858-33a6fdb99642logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[51,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;,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Flogseq____&quot;,45,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Vlogseq____&quot;,42,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-f9b6-4236-8d18-31eee2c7cb68logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[pq-Formel]]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;,68,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Vlogseq____&quot;,68,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,37,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Hlogseq____&quot;,37,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-0348-4ce0-8304-3ca076cd27f8logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Flogseq____&quot;,71,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Vlogseq____&quot;,78,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,25,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,30,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Hlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-4d2f-421d-ac90-f9537e9ffa9blogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\n(a+b)^3(a^2+b^2)^3(a-b)^3logseq____&amp;=(a^2+b^2)^3\\\\left((a+b)(a-b)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=(a^2+b^2)^3(a^2-b^2)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=\\\\left((a^2+b^2)(a^2-b^2)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=(a^4-b^4)^3\\\\\\\\\\n\\\\frac{a-b}{(a+b)^{-1}}logseq____&amp;=(a-b)(a+b)\\\\notag\\\\\\\\\\nlogseq____&amp;=a^2-b^2\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Flogseq____&quot;,72,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Vlogseq____&quot;,70,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-ce45-4d10-9501-2c1bd90af4fflogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[55,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;,[55,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Flogseq____&quot;,57,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Vlogseq____&quot;,79,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-4c7d-4120-b842-ddee35eef5b8logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Rationalmachen]] des [[Nenner]]slogseq____&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;,51,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Vlogseq____&quot;,42,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,34,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,38,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Hlogseq____&quot;,34,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Hlogseq____&quot;,38,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-176e-495b-8d94-b3ce96051cf6logseq____&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;,79,536870918]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Vlogseq____&quot;,79,536870918]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-70c3-491b-ab76-d9f80d54cad7logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Quadratische Gleichungen]]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;,42,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Vlogseq____&quot;,64,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,26,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[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;,26,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-7d52-4632-9843-69a65308de61logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____&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;,40,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Vlogseq____&quot;,40,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,25,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,28,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,30,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Hlogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-f345-41d3-b70d-096e6189aadelogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Allgemein}$\\n\\\\begin{align}\\n\\\\ln a + \\\\ln b logseq____&amp;= \\\\ln(a*b) \\\\\\\\\\n\\\\ln(-a) logseq____&amp;= \\\\frac1{\\\\ln a}\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Flogseq____&quot;,50,536870918]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Vlogseq____&quot;,81,536870918]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Ulogseq____&quot;,27,536870918]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-8120-468b-a88d-cd780a0081a0logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[61,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;,[61,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Flogseq____&quot;,75,536870918]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Vlogseq____&quot;,75,536870918]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,30,536870918]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[61,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-2270-48d3-b0a1-0e465ee5438flogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\frac12 \\\\sqrt2, \\\\frac12, \\\\frac12\\\\sqrt3 \\\\text{ sind werte von }\\\\sin x$\\n\\\\begin{align}\\n\\\\sin 30\\\\degreelogseq____&amp;=\\\\frac12\\\\\\\\\\n\\\\sin 45\\\\degree logseq____&amp;= \\\\frac12\\\\sqrt2 \\\\\\\\\\n\\\\sin 60\\\\degree logseq____&amp;= \\\\frac12 \\\\sqrt3 \\\\\\\\\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Flogseq____&quot;,43,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Vlogseq____&quot;,43,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[62,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-deac-46fa-a85a-368b32a83256logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Was ist Größer?logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Flogseq____&quot;,79,536870918]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Vlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870918]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[63,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-959c-4cbe-a313-87a389fc9447logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Potenzen]] und [[Wurzeln]]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;,75,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Vlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Hlogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Hlogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-871a-4d7f-9321-0dee6d9afc2blogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Welche }$[[Gleichungen]]$\\\\text{ sind richtig?}$\\n\\\\begin{align}\\ne^{x+y} logseq____&amp;= e^x + e^y logseq____&amp; ,f \\\\\\\\\\ne^{x+y} logseq____&amp;= e^x * x^y logseq____&amp; ,r \\\\\\\\\\ne^{x+y}logseq____&amp;=e^{xy} logseq____&amp; ,f\\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=x+y logseq____&amp; ,x+ylogseq____&gt;c \\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=e^x*e^ylogseq____&amp;,f\\\\\\\\\\ne^{ln(x+y)}logseq____&amp;=ln(e^x+y)logseq____&amp;,x+ylogseq____&gt;0\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Flogseq____&quot;,76,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Vlogseq____&quot;,76,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,29,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Hlogseq____&quot;,29,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-c67b-49ab-a806-6e7e138b6fc0logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\n\\\\sqrt{x^4+6x^2y+9y^2}logseq____&amp;=\\\\sqrt{(x^2+3y)^2}=x^2+3y\\\\\\\\\\n\\\\sqrt {x + \\\\sqrt{x^2-y^2}}\\\\sqrt{x-\\\\sqrt{x^2-y^2}}logseq____&amp;=\\\\sqrt{\\\\left(x + \\\\sqrt{x^2-y^2}\\\\right)\\\\left(x-\\\\sqrt{x^2-y^2}\\\\right)}\\\\notag\\\\\\\\\\nlogseq____&amp;=\\\\sqrt{x^2-(x^2-y^2)}\\\\notag\\\\\\\\\\nlogseq____&amp;=\\\\sqrt{y^2}=\\\\left|y\\\\right|\\\\\\\\\\n\\\\sqrt[5]{a\\\\sqrt[3]a}=\\\\sqrt[5]{\\\\sqrt[3]{a^3}\\\\sqrt[3]a}\\nlogseq____&amp;=\\\\sqrt[5]{\\\\sqrt[3]{a^4}}\\n=\\\\sqrt[5]{a^\\\\frac43}\\n=a^{\\\\frac43\\\\frac15}=a^\\\\frac4{15}\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Flogseq____&quot;,73,536870918]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Vlogseq____&quot;,42,536870918]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-f31b-476f-a7b6-ffdf980f00aelogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{array}{c} (a+b)^0logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;1 \\\\\\\\\\n(a+b)^1logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;1 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^2logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 2 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^3logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp;1 logseq____&amp;logseq____&amp; 3 logseq____&amp;logseq____&amp; 3 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^4logseq____&amp;logseq____&amp;logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 4 logseq____&amp;logseq____&amp; 6 logseq____&amp;logseq____&amp; 4 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^5logseq____&amp;logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 5 logseq____&amp;logseq____&amp; 10 logseq____&amp;logseq____&amp; 10 logseq____&amp;logseq____&amp; 5 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^6logseq____&amp;logseq____&amp; 1 logseq____&amp;logseq____&amp; 6 logseq____&amp;logseq____&amp; 15 logseq____&amp;logseq____&amp; 20 logseq____&amp;logseq____&amp; 15 logseq____&amp;logseq____&amp; 6 logseq____&amp;logseq____&amp; 1 \\\\\\\\\\n(a+b)^7logseq____&amp;1 logseq____&amp;logseq____&amp; 7 logseq____&amp;logseq____&amp;21 logseq____&amp;logseq____&amp; 35 logseq____&amp;logseq____&amp; 35 logseq____&amp;logseq____&amp; 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} x=\\\\frac25 \\\\text{ und } y=\\\\frac37 \\\\text{ ist }\\\\frac xy$\\n\\\\begin{align}\\n\\\\frac xy = \\\\frac{\\\\frac25}{\\\\frac37} = 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[[Potenzen]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Flogseq____&quot;,64,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Vlogseq____&quot;,64,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^Hlogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[70,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-9864-42f8-bde8-6a27cc832654logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\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;,[71,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Flogseq____&quot;,67,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Vlogseq____&quot;,78,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,25,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,30,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[71,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-06ec-4398-9905-06008ea29867logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[72,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\na^nlogseq____&amp;=\\\\underbrace{a*a*\\\\cdots*n}_n logseq____&amp; a,blogseq____&gt;0\\\\\\\\\\na^2b^2logseq____&amp;=(ab)^n\\\\\\\\\\n\\\\frac{a^n}{b^n}logseq____&amp;=\\\\left(\\\\frac 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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;,[73,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Flogseq____&quot;,46,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Vlogseq____&quot;,42,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[73,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-cbfb-4996-8c7e-e4e69e8e8b33logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[74,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel 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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 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Formeln]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Flogseq____&quot;,49,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Vlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,30,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^Hlogseq____&quot;,30,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[75,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-aa60-4d94-8e79-38717264bdd0logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Potenzen]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Flogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Vlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[76,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Pascalsches Dreieck]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Flogseq____&quot;,74,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Vlogseq____&quot;,75,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,25,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,30,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[78,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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Aussagen]]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;,137,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Vlogseq____&quot;,119,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Hlogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-27b2-40b8-a2d2-feb0d8060b6elogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel: Bestimmung des }$[[Wahrheitswerteverlauf]]$\\\\text{ von }(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)$\\n|$p$|$q$||$p\\\\rightarrow q$|$q\\\\rightarrow p$|$(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)|$p\\\\leftrightarrow q$|\\n|f|f||w|w|w|w|\\n|f|w||w|f|f|f|\\n|w|f||f|w|f|f|\\n|w|w||w|w|w|w|logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Flogseq____&quot;,130,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Vlogseq____&quot;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,98,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Hlogseq____&quot;,98,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-cfe1-4bc1-b10a-8f07f182076blogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wikipedia]]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;,129,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Vlogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,100,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^Hlogseq____&quot;,100,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[122,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-fd45-477c-a2e4-9e53146411cdlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Belegung]] (der Variablen): Zuordnung von $w/f$ an jede [[Variable]] einer [[Aussageformel]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Flogseq____&quot;,127,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Vlogseq____&quot;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,108,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,116,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Hlogseq____&quot;,108,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Hlogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Hlogseq____&quot;,116,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-87f7-45a1-9a58-6b170d2f0d14logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Aussagenlogische variable]]: [[Variable]], die den Wert $w$ oder $f$ annimmtlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Flogseq____&quot;,135,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Vlogseq____&quot;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,99,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,108,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Hlogseq____&quot;,99,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Hlogseq____&quot;,108,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-d6d6-4e3e-a0ee-a82ec0a34a33logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\np\\\\land q\\\\lor r\\\\\\\\\\n(p\\\\land q)\\\\lor r\\\\\\\\\\np\\\\land (q\\\\lor r)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Flogseq____&quot;,133,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Vlogseq____&quot;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-dd0f-4512-9f35-6e68b54b2e77logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Satz, der wahr oder falsch ist, d.h. der [[Wahrheitswert]] $w$ bzw $f$ hat ($t/f$, $1/0$, $\\\\text{wahr}/\\\\text{falsch}$)logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Flogseq____&quot;,119,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Vlogseq____&quot;,119,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,102,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Hlogseq____&quot;,102,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-1c1e-4e0a-a488-529be73c6930logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Aussageformel]]: Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Flogseq____&quot;,124,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Vlogseq____&quot;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,36,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,111,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Hlogseq____&quot;,36,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Hlogseq____&quot;,111,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Hlogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-9aec-49c8-aaf9-7e08c3f6c3f1logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Tantologie]]: Formel, die konstant $w$ istlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Flogseq____&quot;,121,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Vlogseq____&quot;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,104,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Hlogseq____&quot;,104,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-37af-46df-abd2-2b6b85018951logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;C. Meinel, M. Mundhenk,  [[\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. Auflage 2011]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Flogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Vlogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,103,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Hlogseq____&quot;,103,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-2177-4d67-bc60-017c560a0609logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wahrheitswerteverlauf]] einer [[Aussageformel]]: Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Flogseq____&quot;,123,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Vlogseq____&quot;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,98,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,101,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,102,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,109,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,116,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Hlogseq____&quot;,98,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Hlogseq____&quot;,101,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Hlogseq____&quot;,102,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Hlogseq____&quot;,109,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Hlogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Hlogseq____&quot;,116,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-8015-4b41-801d-c86956c8fc0dlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Flogseq____&quot;,118,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Vlogseq____&quot;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,104,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Hlogseq____&quot;,104,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-a8de-4ff0-bf15-1a77cd36f345logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Büchertiplogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Flogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Vlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^17logseq____&quot;,false,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-def7-43a4-aa4c-1edd5f4bdf57logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sind $p$ und $q$ [[Aussagen]], so auch\\n\\\\begin{align}\\n(p\\\\land q) logseq____&amp;\\\\quadlogseq____&amp; (\\logseq____&quot;\\\\text{und}\\logseq____&quot;)\\\\\\\\\\n(p\\\\lor q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{oder}\\logseq____&quot;)\\\\\\\\\\n(\\\\neg p) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{nicht}\\logseq____&quot;)\\\\\\\\\\n(p\\\\rightarrow q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{impliziert}\\logseq____&quot;)\\\\\\\\\\n(p\\\\leftrightarrow q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{genau dann wenn}\\logseq____&quot;)\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Flogseq____&quot;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Vlogseq____&quot;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Hlogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-2346-43d9-bc08-d487d998d562logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Weitere Beispiel}$\\n\\\\begin{align}\\n(p\\\\rightarrow q)logseq____&amp;\\\\equiv((\\\\neg q)\\\\rightarrow(\\\\neg p))\\\\\\\\\\n(p\\\\land(p\\\\rightarrow q)) logseq____&amp;\\\\rightarrow q logseq____&amp;\\\\quad \\\\text{Tantologie}\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Flogseq____&quot;,131,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Vlogseq____&quot;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-14de-4e7c-a658-57969bcd7a96logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Soweit die \\logseq____&quot;[[Syntax]]\\logseq____&quot;, jetzt die [[Semantik]]. Die [[Wahrheitswert]]e\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Flogseq____&quot;,125,536870921]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Vlogseq____&quot;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Ulogseq____&quot;,102,536870921]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Ulogseq____&quot;,106,536870921]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Ulogseq____&quot;,109,536870921]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Ulogseq____&quot;,113,536870921]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Hlogseq____&quot;,102,536870921]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Hlogseq____&quot;,106,536870921]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Hlogseq____&quot;,109,536870921]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Hlogseq____&quot;,113,536870921]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-ef9e-4a6c-bc76-137f7abe44ealogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[136,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Kontradiktion]]: Formel, die konstant $f$ istlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[136,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[136,logseq____&quot;^Flogseq____&quot;,128,536870921]],[logseq____&quot;^15logseq____&quot;,[136,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[136,logseq____&quot;^Vlogseq____&quot;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[136,logseq____&quot;^Ulogseq____&quot;,105,536870921]],[logseq____&quot;^15logseq____&quot;,[136,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[136,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[136,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[136,logseq____&quot;^Hlogseq____&quot;,105,536870921]],[logseq____&quot;^15logseq____&quot;,[136,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[136,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-5f6e-45bb-8865-f89409d5becalogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[137,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;,536870921]],[logseq____&quot;^15logseq____&quot;,[137,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[137,logseq____&quot;^Flogseq____&quot;,126,536870921]],[logseq____&quot;^15logseq____&quot;,[137,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[137,logseq____&quot;^Vlogseq____&quot;,119,536870921]],[logseq____&quot;^15logseq____&quot;,[137,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[137,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[137,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[137,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-3d94-4371-aa9c-d8e2f278dee4logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Klogseq____&quot;,1696963931001,536870922]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^@logseq____&quot;,false,536870922]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;grundlagen und diskrete strukturenlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^11logseq____&quot;,logseq____&quot;Grundlagen und Diskrete Strukturenlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^Blogseq____&quot;,1696963931001,536870922]],[logseq____&quot;^15logseq____&quot;,[139,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5b-864c-4391-a5e0-e18420c2f9eelogseq____&quot;,536870927]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Grundlagen und Diskrete Strukturen 1]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Flogseq____&quot;,139,536870922]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Xlogseq____&quot;,139,536870922]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Vlogseq____&quot;,139,536870922]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Ulogseq____&quot;,117,536870922]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Ulogseq____&quot;,139,536870922]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^Hlogseq____&quot;,117,536870922]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[140,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5a-c982-47f3-a87a-9c80eccf6e2flogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Klogseq____&quot;,1696963931008,536870923]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^@logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;logarithmusgesetzelogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^11logseq____&quot;,logseq____&quot;Logarithmusgesetzelogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Blogseq____&quot;,1696963931008,536870923]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5b-2dc0-4070-b3a4-07541e52e20blogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Logarithmusgesetze]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Flogseq____&quot;,27,536870923]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Xlogseq____&quot;,27,536870923]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Vlogseq____&quot;,27,536870923]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Ulogseq____&quot;,27,536870923]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Ulogseq____&quot;,142,536870923]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Hlogseq____&quot;,142,536870923]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5b-f3ef-476c-af2e-b1eed45661felogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Flogseq____&quot;,143,536870923]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Xlogseq____&quot;,27,536870923]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Vlogseq____&quot;,27,536870923]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Ulogseq____&quot;,27,536870923]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259d5b-8e30-4919-95dd-f1670b8ca446logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Klogseq____&quot;,1696963931078,536870926]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^@logseq____&quot;,false,536870926]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;programmierung 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Dreiecklogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[33,logseq____&quot;^Blogseq____&quot;,1696964323625,536870918]],[logseq____&quot;^15logseq____&quot;,[33,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-a66b-49c5-ab18-48cf7e46c655logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[34,logseq____&quot;^Klogseq____&quot;,1696964323629,536870918]],[logseq____&quot;^15logseq____&quot;,[34,logseq____&quot;^@logseq____&quot;,false,536870918]],[logseq____&quot;^15logseq____&quot;,[34,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;rationalmachenlogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[34,logseq____&quot;^11logseq____&quot;,logseq____&quot;Rationalmachenlogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[34,logseq____&quot;^Blogseq____&quot;,1696964323629,536870918]],[logseq____&quot;^15logseq____&quot;,[34,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-e694-4ff2-ae64-f15baee09c98logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[35,logseq____&quot;^Klogseq____&quot;,1696964323626,536870918]],[logseq____&quot;^15logseq____&quot;,[35,logseq____&quot;^@logseq____&quot;,false,536870918]],[logseq____&quot;^15logseq____&quot;,[35,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;auffrischung mathe 1logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[35,logseq____&quot;^11logseq____&quot;,logseq____&quot;Auffrischung Mathe 1logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[35,logseq____&quot;^Blogseq____&quot;,1696964323626,536870918]],[logseq____&quot;^15logseq____&quot;,[35,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-537a-4e71-bbe0-e26a3f472f33logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[36,logseq____&quot;^Klogseq____&quot;,1696964323627,536870918]],[logseq____&quot;^15logseq____&quot;,[36,logseq____&quot;^@logseq____&quot;,false,536870918]],[logseq____&quot;^15logseq____&quot;,[36,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;fixmelogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[36,logseq____&quot;^11logseq____&quot;,logseq____&quot;FIXMElogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[36,logseq____&quot;^Blogseq____&quot;,1696964323627,536870918]],[logseq____&quot;^15logseq____&quot;,[36,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-0dfe-447e-8660-c0272d148136logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[37,logseq____&quot;^Klogseq____&quot;,1696964323630,536870918]],[logseq____&quot;^15logseq____&quot;,[37,logseq____&quot;^@logseq____&quot;,false,536870918]],[logseq____&quot;^15logseq____&quot;,[37,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;pq-formellogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[37,logseq____&quot;^11logseq____&quot;,logseq____&quot;pq-Formellogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[37,logseq____&quot;^Blogseq____&quot;,1696964323630,536870918]],[logseq____&quot;^15logseq____&quot;,[37,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-d246-4c5a-a7d9-016ff8ceab84logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[38,logseq____&quot;^Klogseq____&quot;,1696964323628,536870918]],[logseq____&quot;^15logseq____&quot;,[38,logseq____&quot;^@logseq____&quot;,false,536870918]],[logseq____&quot;^15logseq____&quot;,[38,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;nennerlogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[38,logseq____&quot;^11logseq____&quot;,logseq____&quot;Nennerlogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[38,logseq____&quot;^Blogseq____&quot;,1696964323628,536870918]],[logseq____&quot;^15logseq____&quot;,[38,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-dddc-4fac-b449-2cf8aefdc13elogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[39,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;,536870918]],[logseq____&quot;^15logseq____&quot;,[39,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[39,logseq____&quot;^Flogseq____&quot;,46,536870918]],[logseq____&quot;^15logseq____&quot;,[39,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[39,logseq____&quot;^Vlogseq____&quot;,46,536870918]],[logseq____&quot;^15logseq____&quot;,[39,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[39,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[39,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[39,logseq____&quot;^Ulogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[39,logseq____&quot;^Hlogseq____&quot;,36,536870918]],[logseq____&quot;^15logseq____&quot;,[39,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[39,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-1f06-4b9f-ac0b-9f1f11088150logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[40,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\n(a+b)^3(a^2+b^2)^3(a-b)^3logseq____&amp;=(a^2+b^2)^3\\\\left((a+b)(a-b)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=(a^2+b^2)^3(a^2-b^2)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=\\\\left((a^2+b^2)(a^2-b^2)\\\\right)^3\\\\notag\\\\\\\\\\nlogseq____&amp;=(a^4-b^4)^3\\\\\\\\\\n\\\\frac{a-b}{(a+b)^{-1}}logseq____&amp;=(a-b)(a+b)\\\\notag\\\\\\\\\\nlogseq____&amp;=a^2-b^2\\n\\\\end{align}logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[40,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[40,logseq____&quot;^Flogseq____&quot;,47,536870918]],[logseq____&quot;^15logseq____&quot;,[40,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[40,logseq____&quot;^Vlogseq____&quot;,48,536870918]],[logseq____&quot;^15logseq____&quot;,[40,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[40,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[40,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[40,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[40,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-5e62-4cce-8b24-1cef046a4aa3logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[41,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Trigonometrie]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[41,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[41,logseq____&quot;^Flogseq____&quot;,56,536870918]],[logseq____&quot;^15logseq____&quot;,[41,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[41,logseq____&quot;^Vlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[41,logseq____&quot;^Ulogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[41,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[41,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;~:headinglogseq____&quot;,1],536870918]],[logseq____&quot;^15logseq____&quot;,[41,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[41,logseq____&quot;^Hlogseq____&quot;,31,536870918]],[logseq____&quot;^15logseq____&quot;,[41,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[41,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-c77e-4e4b-ad4c-42ec7ed9a361logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[42,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[42,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[42,logseq____&quot;^Flogseq____&quot;,59,536870918]],[logseq____&quot;^15logseq____&quot;,[42,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[42,logseq____&quot;^Vlogseq____&quot;,59,536870918]],[logseq____&quot;^15logseq____&quot;,[42,logseq____&quot;^Ulogseq____&quot;,25,536870918]],[logseq____&quot;^15logseq____&quot;,[42,logseq____&quot;^Ulogseq____&quot;,28,536870918]],[logseq____&quot;^15logseq____&quot;,[42,logseq____&quot;^Ulogseq____&quot;,30,536870918]],[logseq____&quot;^15logseq____&quot;,[42,logseq____&quot;^Ulogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[42,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[42,logseq____&quot;^Hlogseq____&quot;,33,536870918]],[logseq____&quot;^15logseq____&quot;,[42,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[42,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-c070-49fa-869a-41ece1d98612logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[43,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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Gleichungen sind richtig?}$\\n$\\\\text{Wenn }alogseq____&gt;0\\\\text{, 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[[Binomische Formeln]]logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Flogseq____&quot;,41,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Vlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,30,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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[[Logarithmen]]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;,75,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Vlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,27,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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{x + \\\\sqrt{x^2-y^2}}\\\\sqrt{x-\\\\sqrt{x^2-y^2}}logseq____&amp;=\\\\sqrt{\\\\left(x + 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} x=\\\\frac25 \\\\text{ und } y=\\\\frac37 \\\\text{ ist }\\\\frac xy$\\n\\\\begin{align}\\n\\\\frac xy = \\\\frac{\\\\frac25}{\\\\frac37} = 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[[Nenner]]slogseq____&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;,50,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Vlogseq____&quot;,46,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,34,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^Ulogseq____&quot;,38,536870918]],[logseq____&quot;^15logseq____&quot;,[64,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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Gleichungen]]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;,46,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Vlogseq____&quot;,58,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,26,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Jlogseq____&quot;,[],536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^Hlogseq____&quot;,26,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[65,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-823d-44e6-a5f2-fda535b59c0alogseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[66,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;,[66,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Flogseq____&quot;,39,536870918]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Xlogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Vlogseq____&quot;,46,536870918]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,24,536870918]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,32,536870918]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^Ulogseq____&quot;,35,536870918]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^17logseq____&quot;,true,536870918]],[logseq____&quot;^15logseq____&quot;,[66,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-fa0e-4a55-b0b4-ec1b85d2fcd7logseq____&quot;,536870918]],[logseq____&quot;^15logseq____&quot;,[67,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\n\\\\underbrace{\\\\frac6{2+\\\\sqrt2}*\\\\frac{2-\\\\sqrt2}{2-\\\\sqrt2}\\n= \\\\frac{6(2-\\\\sqrt2)}{2^2-(\\\\sqrt2)^2}}_\\\\text{3. binomische Formel}\\nlogseq____&amp;=\\\\frac{6(2-\\\\sqrt2)}2=3(2-\\\\sqrt2)\\\\\\\\\\n\\\\frac{a-b}{\\\\sqrt a+\\\\sqrt b}logseq____&amp;=\\\\frac{a-b}{\\\\sqrt a + \\\\sqrt b}\\\\frac{\\\\sqrt a-\\\\sqrt b}{\\\\sqrt a-\\\\sqrt b}logseq____&amp;, a,b,logseq____&gt;0\\\\notag\\\\\\\\\\n=\\\\frac{(a-b)(\\\\sqrt a-\\\\sqrt b)}{(a-b)}logseq____&amp;=\\\\sqrt a\\\\sqrt 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logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^17logseq____&quot;,false,536870921]],[logseq____&quot;^15logseq____&quot;,[119,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-f33b-43fc-8ac4-80000496c07blogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel: Bestimmung des }$[[Wahrheitswerteverlauf]]$\\\\text{ von }(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)$\\n|$p$|$q$||$p\\\\rightarrow q$|$q\\\\rightarrow p$|$(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)|$p\\\\leftrightarrow q$|\\n|f|f||w|w|w|w|\\n|f|w||w|f|f|f|\\n|w|f||f|w|f|f|\\n|w|w||w|w|w|w|logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Flogseq____&quot;,124,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Vlogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Ulogseq____&quot;,98,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^Hlogseq____&quot;,98,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[120,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-bd33-46d5-8571-4cc585492035logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Kontradiktion]]: Formel, die konstant $f$ istlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Flogseq____&quot;,128,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Vlogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,105,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^Hlogseq____&quot;,105,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[121,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-4d33-4700-94d3-8528a6b2ab07logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[122,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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$p$ und $q$ [[Aussagen]], so auch\\n\\\\begin{align}\\n(p\\\\land q) logseq____&amp;\\\\quadlogseq____&amp; (\\logseq____&quot;\\\\text{und}\\logseq____&quot;)\\\\\\\\\\n(p\\\\lor q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{oder}\\logseq____&quot;)\\\\\\\\\\n(\\\\neg p) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{nicht}\\logseq____&quot;)\\\\\\\\\\n(p\\\\rightarrow q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{impliziert}\\logseq____&quot;)\\\\\\\\\\n(p\\\\leftrightarrow q) logseq____&amp;logseq____&amp; (\\logseq____&quot;\\\\text{genau dann wenn}\\logseq____&quot;)\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Flogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Vlogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^Hlogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[123,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-0830-41d5-b88e-4b94bac6d9d7logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wahrheitswerteverlauf]] einer [[Aussageformel]]: Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Flogseq____&quot;,131,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Vlogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,98,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,101,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,102,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,109,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,116,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Hlogseq____&quot;,98,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Hlogseq____&quot;,101,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Hlogseq____&quot;,102,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Hlogseq____&quot;,109,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Hlogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Hlogseq____&quot;,116,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-1d69-4028-85a5-496feaf618a0logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Aussagenlogische variable]]: [[Variable]], die den Wert $w$ oder $f$ annimmtlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Flogseq____&quot;,134,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Vlogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,99,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,108,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Hlogseq____&quot;,99,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Hlogseq____&quot;,108,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-e83e-4a43-b6b7-693e9369408dlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Flogseq____&quot;,127,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Vlogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,104,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Hlogseq____&quot;,104,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-2173-46ad-8bfe-54ae0a26a09alogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formeln $p,q$ [[logisch äquivalent]], wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Flogseq____&quot;,121,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Vlogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,98,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,107,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,115,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Hlogseq____&quot;,98,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Hlogseq____&quot;,107,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Hlogseq____&quot;,115,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-862c-4995-863a-5d9ed81f8134logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Tantologie]]: Formel, die konstant $w$ istlogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Flogseq____&quot;,120,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Vlogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,104,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Hlogseq____&quot;,104,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-c5ee-4f4c-85ed-fa53c3d4c484logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wikipedia]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Flogseq____&quot;,135,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Vlogseq____&quot;,119,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,100,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Hlogseq____&quot;,100,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-9716-47ee-bfc0-f4537d4d57f3logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Weitere Beispiel}$\\n\\\\begin{align}\\n(p\\\\rightarrow q)logseq____&amp;\\\\equiv((\\\\neg q)\\\\rightarrow(\\\\neg p))\\\\\\\\\\n(p\\\\land(p\\\\rightarrow q)) logseq____&amp;\\\\rightarrow q logseq____&amp;\\\\quad \\\\text{Tantologie}\\n\\\\end{align}logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Flogseq____&quot;,126,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Vlogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-28a0-4c10-b07f-ac60da285e46logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Belegung]] (der Variablen): Zuordnung von $w/f$ an jede [[Variable]] einer [[Aussageformel]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Flogseq____&quot;,133,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Vlogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,108,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,116,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Hlogseq____&quot;,108,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Hlogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^Hlogseq____&quot;,116,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[131,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-0b16-486f-b67b-caceabc16f45logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Verknüpfung von Aussagen]]logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Flogseq____&quot;,137,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Vlogseq____&quot;,136,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Jlogseq____&quot;,[],536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^Hlogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[132,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-2c23-44fb-8d98-e40fdfa598d1logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Aussageformel]]: Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Flogseq____&quot;,125,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Vlogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Ulogseq____&quot;,36,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Ulogseq____&quot;,111,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Ulogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Hlogseq____&quot;,36,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Hlogseq____&quot;,111,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^Hlogseq____&quot;,112,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[133,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-ed4e-470e-b4f1-ef090279c53clogseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Soweit die \\logseq____&quot;[[Syntax]]\\logseq____&quot;, jetzt die [[Semantik]]. Die [[Wahrheitswert]]e\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Flogseq____&quot;,118,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Xlogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Vlogseq____&quot;,132,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Ulogseq____&quot;,102,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Ulogseq____&quot;,106,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Ulogseq____&quot;,109,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Ulogseq____&quot;,110,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Ulogseq____&quot;,113,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Ulogseq____&quot;,114,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Ulogseq____&quot;,117,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Hlogseq____&quot;,102,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Hlogseq____&quot;,106,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Hlogseq____&quot;,109,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^Hlogseq____&quot;,113,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^17logseq____&quot;,true,536870921]],[logseq____&quot;^15logseq____&quot;,[134,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65259ee3-0f8a-431a-a07b-a32d03884380logseq____&quot;,536870921]],[logseq____&quot;^15logseq____&quot;,[135,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;C. Meinel, M. Mundhenk,  [[\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. 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