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[[Quadratische Gleichungen]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Flogseq____&quot;,80,536870919]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Vlogseq____&quot;,82,536870919]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[48,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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constraintlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Flogseq____&quot;,80,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Vlogseq____&quot;,80,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Ulogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^Hlogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[49,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd1-33c7-4205-8645-0bd52fb7f906logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel}$\\n\\\\begin{align}\\nx^4-34x^2+225logseq____&amp;=0\\\\\\\\\\n\\\\text{substituiert }ylogseq____&amp;=x^2\\\\\\\\\\ny^2-34y+225logseq____&amp;=0\\\\\\\\\\ny_{1,2}logseq____&amp;=17\\\\pm\\\\sqrt{(-17)^2-225}\\\\\\\\\\nlogseq____&amp;=17\\\\pm\\\\sqrt{289-225}\\nlogseq____&amp;=17\\\\pm\\\\sqrt{64}=17\\\\pm8\\\\\\\\\\nlogseq____&amp;=\\\\left.\\\\begin{cases}\\n25\\\\\\\\\\n9\\n\\\\end{cases}\\\\right|\\\\begin{array}{l}\\nx^2=25logseq____&amp;\\\\rightarrow logseq____&amp;x_1=5;logseq____&amp;x_2=-5\\\\\\\\\\nx^2=9logseq____&amp;\\\\rightarrow logseq____&amp;x_1=3;logseq____&amp;x_2=-3\\\\\\\\\\n\\\\end{array}\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Flogseq____&quot;,81,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Vlogseq____&quot;,58,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[50,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd1-af41-4fd3-806c-4edd226d0a83logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Alte Schreibweise}$\\n\\\\begin{align}\\n\\\\text{cosa }logseq____&amp;\\\\text{plus }logseq____&amp;\\\\text{cubus }logseq____&amp;\\\\text{acq }logseq____&amp;6\\\\\\\\\\nxlogseq____&amp;+logseq____&amp;x^3logseq____&amp;=logseq____&amp;6\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Flogseq____&quot;,61,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Vlogseq____&quot;,88,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[51,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd1-852f-430a-a96d-1e2034f5c8c1logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nax^2+bx+clogseq____&amp;=0logseq____&amp;|:a\\\\quadlogseq____&amp;a\\\\ne0\\\\\\\\\\nx^2+\\\\frac ba x + \\\\frac ca logseq____&amp;= 0\\\\\\\\\\nplogseq____&amp;=\\\\frac ba,logseq____&amp;q = \\\\frac ca\\\\\\\\\\nx^2+px+qlogseq____&amp;=0\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Flogseq____&quot;,48,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Vlogseq____&quot;,48,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[52,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd1-c382-42fd-bd00-a8b0c50046e1logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[53,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;,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Flogseq____&quot;,95,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Vlogseq____&quot;,69,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[53,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd1-b99e-4aa0-a495-ac0ce40ab896logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Flogseq____&quot;,85,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Vlogseq____&quot;,85,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ulogseq____&quot;,28,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Ulogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^Hlogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[54,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd1-d9c1-4087-999c-3f29d9f32b8clogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Flogseq____&quot;,91,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Vlogseq____&quot;,91,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Ulogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^Hlogseq____&quot;,41,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[55,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd1-7dcc-4909-9b5c-b029c08dd9bdlogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# Wissensabgleich [[Trigonometrie]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Flogseq____&quot;,97,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Vlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^Hlogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[56,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd1-80db-4916-bb9f-d566f45bab90logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Rationalmachen]] des [[Nenner]]slogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Flogseq____&quot;,90,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Vlogseq____&quot;,80,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,38,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Ulogseq____&quot;,44,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Hlogseq____&quot;,38,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^Hlogseq____&quot;,44,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[57,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd1-e64e-43ce-b20d-cee9b788f83flogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[pq-Formel]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Flogseq____&quot;,52,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Vlogseq____&quot;,48,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,29,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Ulogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^Hlogseq____&quot;,42,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[58,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd1-c4c2-4617-b0ef-21950b7b1698logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[59,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 b\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Flogseq____&quot;,63,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Vlogseq____&quot;,57,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,38,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^Ulogseq____&quot;,44,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[59,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd1-f602-46e5-83d0-bdf451d24bb0logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[60,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Einsetzen, um zu überprüfen, ob man eine Fallunterscheidung 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[[Potenzen]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Flogseq____&quot;,76,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Vlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^Hlogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[83,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd1-48d7-44bc-927c-b757406fca8blogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[84,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Für } x=\\\\frac25 \\\\text{ und } y=\\\\frac37 \\\\text{ ist }\\\\frac xy$\\n\\\\begin{align}\\n\\\\frac xy = \\\\frac{\\\\frac25}{\\\\frac37} = 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x)^5*(1-\\\\sqrt 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[[Binomische Formeln]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Flogseq____&quot;,56,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Vlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^Hlogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[86,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd1-4851-4213-8fd3-a6fc2ffbd618logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel für die 3. Binomische Formel}$\\n\\\\begin{align}\\n\\\\frac{\\\\frac1{a-b}+\\\\frac1{a+b}}{\\\\frac1{a-b}-\\\\frac1{a+b}}\\nlogseq____&amp;=\\\\frac{\\\\frac{a+b+a-b}{(a+b)*(a-b)}}{\\\\frac{a+b-(a-b)}{(a+b)*(a-b)}}\\nlogseq____&amp;=\\\\frac{a+b+a-b}{a+b-a+b}\\nlogseq____&amp;=\\\\frac{2a}{2b}\\nlogseq____&amp;=\\\\frac ab\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Flogseq____&quot;,62,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Vlogseq____&quot;,86,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,34,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[87,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd1-0124-4563-864a-0f5adc4c1f18logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Potenzen]]logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Flogseq____&quot;,82,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Vlogseq____&quot;,82,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,36,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Jlogseq____&quot;,[],536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^Hlogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[88,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd1-50c6-4e22-bd47-014a62932090logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[89,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 + 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\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Flogseq____&quot;,56,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Vlogseq____&quot;,56,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,35,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[92,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd1-2878-488d-b35f-e3168cc63798logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;![draws/2023-10-08-21-23-31.excalidraw](../assets/excalidraw_svg/2023-10-08-21-23-31.svg)logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Flogseq____&quot;,96,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Xlogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Vlogseq____&quot;,83,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,27,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^Ulogseq____&quot;,39,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^17logseq____&quot;,true,536870919]],[logseq____&quot;^15logseq____&quot;,[93,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd1-ddbb-4733-b029-06fd123eac7alogseq____&quot;,536870919]],[logseq____&quot;^15logseq____&quot;,[94,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\na^nlogseq____&amp;=\\\\underbrace{a*a*\\\\cdots*n}_n 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:2\\\\\\\\\\n\\\\end{align}\\n\\\\begin{align}\\nL_2=\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|xlogseq____&lt;3,x\\\\ge-2,x\\\\ge\\\\frac12\\\\right\\\\}=\\\\left[\\\\frac12,3\\\\right)\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Flogseq____&quot;,126,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Xlogseq____&quot;,105,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Vlogseq____&quot;,125,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,100,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,101,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,104,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,105,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,106,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[124,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-ba79-4894-9271-bebee1a0c1b8logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### Lösung mit [[Fallunterscheidung]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Flogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Xlogseq____&quot;,105,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Vlogseq____&quot;,114,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,100,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,101,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,104,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,105,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,106,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Jlogseq____&quot;,[],536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^Hlogseq____&quot;,101,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[125,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-a411-4170-9ded-884c3d012f36logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{2. Fall}\\\\quad xlogseq____&lt;3$\\n\\\\begin{align}\\n|\\\\underbrace{x-3}_{logseq____&lt;0}|logseq____&amp;=6(x-3)=-x+3\\\\\\\\\\n-x+3logseq____&amp;\\\\le|x+2|\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Flogseq____&quot;,121,536870920]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Xlogseq____&quot;,105,536870920]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Vlogseq____&quot;,125,536870920]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,100,536870920]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,101,536870920]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,104,536870920]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,105,536870920]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,106,536870920]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[126,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-6d8b-41bb-aae2-998cd8f7428clogseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Mengen]]logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Flogseq____&quot;,105,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Xlogseq____&quot;,105,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Vlogseq____&quot;,105,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,105,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Jlogseq____&quot;,[],536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^Hlogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^17logseq____&quot;,false,536870920]],[logseq____&quot;^15logseq____&quot;,[127,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-2e82-4d62-8a6d-ab6df3d57f77logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{1. Fall}\\\\quad x\\\\ge3$\\n\\\\begin{align}\\n|x-3|logseq____&amp;=x-3\\\\\\\\\\nx-3\\\\le|x+2|\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Flogseq____&quot;,125,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Xlogseq____&quot;,105,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Vlogseq____&quot;,125,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,100,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,101,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,104,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,105,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,106,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[128,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-7cf2-4b9e-a116-274cc5a45927logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Fall 1a}\\\\quad x\\\\ge -2$\\n\\\\begin{align}\\n|x+2|logseq____&amp;=x+2\\\\\\\\\\nx-3logseq____&amp;\\\\le x+2 logseq____&amp;|logseq____&amp;+3-x\\\\\\\\\\n0logseq____&amp;\\\\le5\\\\\\\\\\n\\\\end{align}\\n\\\\begin{align}\\nL_1=\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|x\\\\ge3,x\\\\ge-2,0\\\\le5\\\\right\\\\}=\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|x\\\\ge3\\\\right\\\\}=[3,\\\\infty)\\n\\\\end{align}logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Flogseq____&quot;,128,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Xlogseq____&quot;,105,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Vlogseq____&quot;,125,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,100,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,101,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,104,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,105,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,106,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^Ulogseq____&quot;,107,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^17logseq____&quot;,true,536870920]],[logseq____&quot;^15logseq____&quot;,[129,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-d092-45dd-9efc-5cee4d896e93logseq____&quot;,536870920]],[logseq____&quot;^15logseq____&quot;,[130,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Menge aller reellen Zahlen zwischen 1 und 4 ohne 1 und 4\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|-1logseq____&lt;xlogseq____&lt;4\\\\right\\\\}=:\\\\underbrace{(-1,4)}_\\\\text{Offenes 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grundlagen der informatik\\logseq____&quot;, 5. auflage 2011logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^11logseq____&quot;,logseq____&quot;\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. Auflage 2011logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^Blogseq____&quot;,1697193426244,536870922]],[logseq____&quot;^15logseq____&quot;,[141,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-44c6-4692-b3d3-0b1ebcd25d0clogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Klogseq____&quot;,1697193426260,536870922]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^@logseq____&quot;,false,536870922]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;tantologielogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^11logseq____&quot;,logseq____&quot;Tantologielogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^Blogseq____&quot;,1697193426260,536870922]],[logseq____&quot;^15logseq____&quot;,[142,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-a73c-4ed5-8515-bbe3aa7de1d3logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Klogseq____&quot;,1697193426258,536870922]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^@logseq____&quot;,false,536870922]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;kontradiktionlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^11logseq____&quot;,logseq____&quot;Kontradiktionlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^Blogseq____&quot;,1697193426258,536870922]],[logseq____&quot;^15logseq____&quot;,[143,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-19a6-4a03-9d31-ff909ac91d82logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Klogseq____&quot;,1697193426254,536870922]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^@logseq____&quot;,false,536870922]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;variablenlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^11logseq____&quot;,logseq____&quot;Variablenlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^Blogseq____&quot;,1697193426254,536870922]],[logseq____&quot;^15logseq____&quot;,[144,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-cf44-401f-9a13-f2cf4510b34blogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[145,logseq____&quot;^Klogseq____&quot;,1697193426248,536870922]],[logseq____&quot;^15logseq____&quot;,[145,logseq____&quot;^@logseq____&quot;,false,536870922]],[logseq____&quot;^15logseq____&quot;,[145,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;semantiklogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[145,logseq____&quot;^11logseq____&quot;,logseq____&quot;Semantiklogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[145,logseq____&quot;^Blogseq____&quot;,1697193426248,536870922]],[logseq____&quot;^15logseq____&quot;,[145,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-2d1a-4a3f-ab4a-bb4d3d2d0d27logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^Klogseq____&quot;,1697193426259,536870922]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^@logseq____&quot;,false,536870922]],[logseq____&quot;^15logseq____&quot;,[146,logseq____&quot;^Ylogseq____&quot;,logseq____&quot;logisch 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von aussagenlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[152,logseq____&quot;^11logseq____&quot;,logseq____&quot;Verknüpfung von 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mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach 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[[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Flogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Vlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Ulogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^Hlogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[156,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-6e7c-4bda-b321-93161b0e3515logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Flogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Vlogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Ulogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Ulogseq____&quot;,149,536870922]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Ulogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Hlogseq____&quot;,41,536870922]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^Hlogseq____&quot;,149,536870922]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[157,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-40d8-4754-adde-11debe2f4b1flogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiel: Bestimmung des }$[[Wahrheitswerteverlauf]]$\\\\text{ von }(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)$\\n|$p$|$q$||$p\\\\rightarrow q$|$q\\\\rightarrow p$|$(p\\\\rightarrow q)\\\\land(q\\\\rightarrow p)|$p\\\\leftrightarrow q$|\\n|-|-|-|-|-|-|\\n|f|f||w|w|w|w|\\n|f|w||w|f|f|f|\\n|w|f||f|w|f|f|\\n|w|w||w|w|w|w|logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Flogseq____&quot;,155,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Vlogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Ulogseq____&quot;,136,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Ulogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^Hlogseq____&quot;,136,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[158,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-8265-4443-8461-ef624280cab1logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\text{Beispiele}$\\n\\\\begin{align}\\nlogseq____&amp;\\logseq____&quot;5\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;\\\\quadlogseq____&amp; (w)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;4\\\\text{ ist prim}\\logseq____&quot; logseq____&amp;logseq____&amp; (f)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Jede gerade Zahl }\\\\ge4\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ ist Summe zweier Primzahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage, }w\\\\text{ oder }f)\\\\notag\\\\\\\\\\nlogseq____&amp;(\\\\text{Vermutung von Goldback 1742})\\\\text{, }logseq____&amp;logseq____&amp;\\\\text{richtig für gerade Zahlen bis }4*10^{18}\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Dieser Satz ist falsch}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{keine Aussage})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Gleichung } x^2+y^2=z^2 \\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ hat eine Lösung }x,y,z\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{ aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp; (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nlogseq____&amp;x^n+y^n=z^n\\\\text{ eine Lösung}logseq____&amp;logseq____&amp; (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nlogseq____&amp;x,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____&quot; logseq____&amp;logseq____&amp;\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Gott ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Nietzsche ist tot}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&amp;\\logseq____&quot;\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____&quot; logseq____&amp;logseq____&amp; (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Flogseq____&quot;,173,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Vlogseq____&quot;,171,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[159,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-9468-4c14-8819-ca54d853692elogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;C. Meinel, M. Mundhenk, [[\\logseq____&quot;Mathematische Grundlagen der Informatik\\logseq____&quot;, 5. Auflage 2011]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Flogseq____&quot;,177,536870922]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Vlogseq____&quot;,177,536870922]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Ulogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^Hlogseq____&quot;,141,536870922]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[160,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-490b-4fd2-9a1e-e9485301d54dlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[161,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;,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Flogseq____&quot;,164,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Vlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[161,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-041c-43eb-8e80-a34e3d0f5091logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Flogseq____&quot;,163,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Vlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^Hlogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[162,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-cf2e-486e-aac2-1e6db0d8868elogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formeln $p,q$ [[logisch äquivalent]], wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Flogseq____&quot;,175,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Vlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ulogseq____&quot;,136,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ulogseq____&quot;,146,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Ulogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Hlogseq____&quot;,136,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Hlogseq____&quot;,146,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^Hlogseq____&quot;,153,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[163,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-d1cc-4f76-b19a-e54c6d54e56flogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[164,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;,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Flogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Vlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^Hlogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[164,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-9b24-41c4-b57c-b0e7a391a148logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Formel, die konstant $f$ istlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Flogseq____&quot;,175,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Vlogseq____&quot;,175,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ulogseq____&quot;,143,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[165,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-5f4e-4d57-9700-eb460fb54b1flogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Aussagenlogische Variable]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Flogseq____&quot;,168,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Vlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,137,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^Hlogseq____&quot;,137,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[166,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-d880-4a87-b111-011edee87137logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Belegung]] (der [[Variablen]])logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Flogseq____&quot;,156,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Vlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,144,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Hlogseq____&quot;,144,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^Hlogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[167,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-d7f2-442b-a6a2-a9c7d60e33a4logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Soweit die \\logseq____&quot;[[Syntax]]\\logseq____&quot;, jetzt die [[Semantik]]. Die [Wahrheitswerte](Wahrheitswert)\\n ergeben sich aus den Wahrheitswerten von $p$,$q$ gemäß folgender Tabelle ([[Tabellenregeln]]).\\n|$p$|$q$||$p\\\\land q$|$p\\\\lor q$|$\\\\neg p$|$p\\\\rightarrow q$|$p\\\\leftrightarrow q$|\\n|---|----||-----------|---------|---------|-----------------|---------------------|\\n|f|f||f|f|w|w|w|\\n|f|w||f|w|w|w|f|\\n|w|f||f|w|f|f|f|\\n|w|w||w|w|f|w|w|logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Flogseq____&quot;,161,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Vlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,145,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,151,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Hlogseq____&quot;,145,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Hlogseq____&quot;,147,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^Hlogseq____&quot;,151,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[168,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-7c06-496c-8daf-b36a15f0948blogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Wikipedia]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Flogseq____&quot;,160,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Vlogseq____&quot;,177,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Ulogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^Hlogseq____&quot;,138,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[169,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-8c54-486a-a7d3-2ebc431ddec7logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Zuordnung von $w/f$ an jede [Variable](Variablen) einer [[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Flogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Vlogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,144,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Ulogseq____&quot;,154,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^Hlogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[170,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-8af9-4470-8574-526d04e2b9e8logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 1. [[Aussagen]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Flogseq____&quot;,177,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Vlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^Hlogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[171,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-9184-417a-ae4c-35521c079345logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Variable](Variablen), die den Wert $w$ oder $f$ annimmtlogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Flogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Vlogseq____&quot;,166,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,137,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[172,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-a7f6-4937-be2e-bfdcd6a1f2aclogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[173,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;,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Flogseq____&quot;,171,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Vlogseq____&quot;,171,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,140,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^Hlogseq____&quot;,140,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[173,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-0bf7-4e10-be60-f51f6bfde7e7logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[174,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 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[[Kontradiktion]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Flogseq____&quot;,176,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Vlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,143,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^Hlogseq____&quot;,143,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[175,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-bb78-4d0f-b92c-7060a303836elogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Tantologie]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Flogseq____&quot;,178,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Vlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,3],536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^Hlogseq____&quot;,142,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^17logseq____&quot;,true,536870922]],[logseq____&quot;^15logseq____&quot;,[176,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-d85e-41a5-a5fa-66736aa95179logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# 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logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^Jlogseq____&quot;,[],536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^17logseq____&quot;,false,536870922]],[logseq____&quot;^15logseq____&quot;,[177,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-559d-40fc-8e6e-3ea6d398252flogseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Flogseq____&quot;,167,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Xlogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Vlogseq____&quot;,180,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,133,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,136,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,148,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,150,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^Ulogseq____&quot;,152,536870922]],[logseq____&quot;^15logseq____&quot;,[178,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ 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p(x)\\\\quadlogseq____&amp;Kontradiktion\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Flogseq____&quot;,215,536870923]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[201,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-8ff2-4738-bea5-36fc66e9890flogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche Regeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Flogseq____&quot;,240,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Vlogseq____&quot;,240,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,183,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,189,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,190,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Ulogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Hlogseq____&quot;,183,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Hlogseq____&quot;,187,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Hlogseq____&quot;,189,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Hlogseq____&quot;,190,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Hlogseq____&quot;,195,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^Hlogseq____&quot;,196,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[202,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-4166-41a5-9c5b-ac02f4ce65d9logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Widerspruch = ↯, #logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Flogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Vlogseq____&quot;,224,536870923]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,191,536870923]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[203,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-ec00-4de6-8bba-fca6a14afec0logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\underbrace{\\\\forall}_\\\\text{Allquantor} x: p(x) logseq____&amp;\\\\equiv p(O_1) \\\\land p(O_2) \\\\land \\\\cdots \\\\land p(O_m)\\\\\\\\\\n\\\\underbrace{\\\\exists}_\\\\text{Existenzquantor} x: p(x) logseq____&amp;\\\\equiv p(0_1) \\\\lor p(O_2) \\\\lor \\\\cdots \\\\lor p(0_m)\\\\\\\\\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Flogseq____&quot;,221,536870923]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[204,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-1aec-426c-9d9a-fedec013afd5logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Verschiedene [[Quantoren]] dürfen **nicht** vertauscht werdenlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Flogseq____&quot;,239,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Vlogseq____&quot;,211,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,191,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^Hlogseq____&quot;,191,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[205,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-8364-4b9c-8243-a616d11df2b0logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $x$ aus $\\\\Reals$ beliebig. Setze $y:=x+1$ (ist aus $\\\\Reals$). Dann ist $xlogseq____&lt;x+1=y$ also $xlogseq____&lt;y$. $\\\\blacksquare$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Flogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Vlogseq____&quot;,227,536870923]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,191,536870923]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[206,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-bce0-400e-994c-0dc646ea2353logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel](Beispiele)logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Flogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[207,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-9bd4-46d3-bf7e-bb8599d81897logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Satz]] mit [[Variablen]] $x_1,\\\\cdots,x_n$, der bei Ersetzung jedes $x_j$ durch ein [Objekt](Objekt (Logik)) aus $U_j$ stets zu einer [Aussage](Aussagen) wirdlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Flogseq____&quot;,214,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,144,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Ulogseq____&quot;,200,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Hlogseq____&quot;,144,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^Hlogseq____&quot;,200,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[208,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-c0df-4c24-8008-854c0566ec04logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\neg\\\\left(\\\\forall x :\\\\exists y :\\\\forall w :\\\\forall u :\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)\\\\right)\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Flogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Vlogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[209,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-f3bd-4830-8f45-24cad100c9f2logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x,y)$ AF in Variablen $x,y$ über $U_1,U_2$\\n\\\\begin{align}\\n\\\\underbrace{\\\\forall x: \\\\underbrace{\\\\exists y: p(x,y)}_{\\\\text{AF in den Variablen }x\\\\text{ über }U_1}}_{\\\\text{Aussage}}\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Flogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Vlogseq____&quot;,233,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,182,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[210,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-f676-483e-8048-15ed9d93b6e2logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\nlogseq____&amp;\\\\forall x: \\\\forall y: p(x, y) \\\\equiv \\\\forall y: \\\\forall x: p(x,y)\\\\\\\\\\nlogseq____&amp;\\\\exists x:\\\\exists y:p(x,y)\\\\equiv\\\\exists y:\\\\exists x:p(x,y)\\\\\\\\\\nlogseq____&amp;[\\\\forall x_1:\\\\forall x_2: \\\\cdots:\\\\forall x_n:p(x_1,x_2,\\\\cdots,x_n)\\\\notag\\\\\\\\\\nlogseq____&amp;\\\\equiv\\\\forall_{x_{\\\\pi(1)}}:\\\\forall_{x_{\\\\pi(1)}}:\\\\cdots:\\\\forall_{x_{\\\\pi(1)}}:p(x_1,x_2,\\\\cdots,x_n)\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Flogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Vlogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,191,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[211,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-a9ff-484c-b969-ddb436f68f17logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\forall x:p(x)$ ist die [Aussage](Aussagen): $\\logseq____&quot;\\\\text{Für alle x aus U ist p(x) wahr}\\logseq____&quot;\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w\\\\quadlogseq____&amp;\\\\text{fallls p(x) w für alle x aus U}\\\\\\\\f\\\\quadlogseq____&amp;\\\\text{falls p(x) f für (wenigstens) ein x aus U}\\\\end{cases}$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Flogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Vlogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,140,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^Hlogseq____&quot;,140,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[212,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-a78b-4514-940c-7770c6d1ead7logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\exists x:p(x)$ ist die Aussage: \\logseq____&quot;Es gibt (wenigstens) ein x aus U für das $p(x)$ wahr ist\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w \\\\quadlogseq____&amp;\\\\text{falls }p(x)\\\\text{ w ist für (wenigstens) ein x aus U}\\\\\\\\f\\\\quad logseq____&amp;\\\\text{falls }p(x)\\\\text{ f ist für alle x aus U}\\\\end{cases}$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Flogseq____&quot;,204,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ulogseq____&quot;,140,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^Hlogseq____&quot;,140,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[213,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-251e-40fd-bf2b-fffec418a6c1logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Aussageform]] (AF) über [Universen](Universen (Logik)) $U_1,\\\\cdots,U_n$:logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Flogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^Hlogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[214,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-b914-45c2-9821-f545bdb79716logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Die beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache](Sprachen) der [[Aussagenlogik]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Flogseq____&quot;,237,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ulogseq____&quot;,185,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^Hlogseq____&quot;,185,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[215,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-bc01-4d41-af09-b1ddfe9d3757logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Gleichartige](Gleichartig) [[Quantoren]] dürfen vertauscht werdenlogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Flogseq____&quot;,238,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ulogseq____&quot;,191,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^Hlogseq____&quot;,191,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[216,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-e0a9-4fe4-9bcf-7bfcb095174alogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Nach Ersetzung von $x$ in der AF $\\logseq____&quot;xlogseq____&lt;y\\logseq____&quot;$ durch eine konkrete Zahl entsteht eine AF in der Variablen $y$, z. Bsp. $\\logseq____&quot;17logseq____&lt;y\\logseq____&quot;$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Flogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Vlogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[217,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-95ff-45af-af04-69936b7c019clogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Aussageform]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Flogseq____&quot;,240,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Vlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^Hlogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[218,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-7b54-4fa9-b24e-2f08b25feb0blogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Allquantor]] [[Existenzquantor]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^Flogseq____&quot;,204,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^Vlogseq____&quot;,204,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^Ulogseq____&quot;,192,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^Ulogseq____&quot;,198,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^Hlogseq____&quot;,192,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^Hlogseq____&quot;,198,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[219,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-fb49-4268-bc0c-00609c80550blogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[220,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[[Beispiele]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[220,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[220,logseq____&quot;^Flogseq____&quot;,208,536870923]],[logseq____&quot;^15logseq____&quot;,[220,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[220,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[220,logseq____&quot;^Ulogseq____&quot;,100,536870923]],[logseq____&quot;^15logseq____&quot;,[220,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[220,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[220,logseq____&quot;^Hlogseq____&quot;,100,536870923]],[logseq____&quot;^15logseq____&quot;,[220,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[220,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-5192-40b0-91c6-f361153b2250logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Endliches Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Flogseq____&quot;,201,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[221,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-9e04-41c7-943a-c90284e9dec6logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;# [[Regeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^Flogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^Vlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^Ulogseq____&quot;,182,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,1],536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^Hlogseq____&quot;,182,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^17logseq____&quot;,false,536870923]],[logseq____&quot;^15logseq____&quot;,[222,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-c952-4e3b-a132-dbb7a3b98f88logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[223,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Betrachte $\\logseq____&quot;xlogseq____&lt;y\\logseq____&quot;$ als AF über $\\\\Reals, 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$y$ aus $\\\\Reals$ mit $xlogseq____&lt;y$ für alle $x$ aus $\\\\Reals$, so insbesondere auch $ylogseq____&lt;y$, Widerspruch. 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ist prim}\\logseq____&quot; \\\\quad logseq____&amp; \\\\text{ist AF mit Variablen x über den natürlichen Zahlen}\\\\\\\\\\n\\logseq____&quot;\\\\underbrace{x}_{x_1}logseq____&lt;\\\\underbrace{y}_{x_2}\\logseq____&quot;\\\\quad logseq____&amp;\\\\text{ist AF mit Variablen }x,y\\\\text{ über die reellen Zahlen } \\\\underbrace{\\\\Reals}_{U_1},\\\\underbrace{\\\\Reals}_{U_2}\\\\\\\\\\n\\logseq____&quot;\\\\text{x ist wahr}\\logseq____&quot;\\\\quadlogseq____&amp;\\\\text{ist AF mit Variablen x über dem Universum der Aussagen}\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^Flogseq____&quot;,220,536870923]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[229,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-53a1-49c0-a25c-c237baa5d4a9logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Flogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Vlogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Ulogseq____&quot;,182,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Ulogseq____&quot;,184,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Ulogseq____&quot;,194,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Ulogseq____&quot;,199,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Hlogseq____&quot;,184,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Hlogseq____&quot;,194,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^Hlogseq____&quot;,199,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[230,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-2045-4302-ae53-3b04ef317373logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;$\\\\blacksquare$ = Beweisende, auch [q.e.d.](Q.E.D.), [[w.z.b.w.]], QED, ![image.png](../assets/image_1697192491775_0.png)logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^Flogseq____&quot;,206,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^Vlogseq____&quot;,206,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^Ulogseq____&quot;,186,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^Ulogseq____&quot;,191,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^Hlogseq____&quot;,186,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[231,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-77b5-4378-93b8-eb7025dbd2aflogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;[Beispiel](Beispiele)logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Flogseq____&quot;,211,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Vlogseq____&quot;,216,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Ulogseq____&quot;,191,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[232,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-452c-47bc-a5ea-714d7acc5b85logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Schachtelung von quantoren ([Beispiel](Beispiele)):logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Flogseq____&quot;,235,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Vlogseq____&quot;,238,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Ulogseq____&quot;,182,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[233,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-4fba-4216-8513-711bc58f110clogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;()logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Flogseq____&quot;,209,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Vlogseq____&quot;,207,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[234,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-4789-416c-a493-6fb5bf49ebe4logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;\\\\begin{align}\\n\\\\forall x:(p(x)\\\\land q(x)) logseq____&amp;\\\\equiv (\\\\forall x: p(x)) \\\\land (\\\\forall x:q(x));\\\\notag\\\\\\\\\\n\\\\exists x: (p(x) \\\\lor q(x)) logseq____&amp;\\\\equiv (\\\\exists x: p(x))\\\\lor(\\\\exists x: q(x)),\\\\quadlogseq____&amp;\\\\text{Große Assoziativgesetze}\\\\\\\\\\n\\\\neg(\\\\forall x:p(x))logseq____&amp;\\\\equiv \\\\exists x: (\\\\neg p(x));\\\\quadlogseq____&amp;\\\\text{Große de Morgansche Regeln;}\\\\notag\\\\\\\\\\n\\\\neg(\\\\exists x: p(x)) logseq____&amp;\\\\equiv \\\\forall x: (\\\\neg p(x)),\\\\quadlogseq____&amp;\\\\text{Negationsregeln.}\\n\\\\end{align}logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Flogseq____&quot;,238,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Vlogseq____&quot;,238,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Ulogseq____&quot;,182,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[235,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-f0a8-467d-acc1-2969b621caaclogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Alternativschreibweisen:\\n$\\\\forall x: p(x)$ auch $\\\\bigger\\\\land x:p(x)$\\n$\\\\exists x:p(x)$ auch $\\\\bigger\\\\lor x:p(x)$logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Flogseq____&quot;,213,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[236,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-c535-4663-8e4d-f7ea6e419f38logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;Sei $p(x)$ AF in der Variablen $x$ über $U$:logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Flogseq____&quot;,229,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[237,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-6c4d-44aa-a942-5830ad3bb127logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;## [[Regeln]]logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ologseq____&quot;,logseq____&quot;^16logseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Flogseq____&quot;,236,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Xlogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Vlogseq____&quot;,218,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,182,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,188,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Ulogseq____&quot;,197,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^?logseq____&quot;,[logseq____&quot;^ logseq____&quot;,logseq____&quot;^18logseq____&quot;,2],536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Jlogseq____&quot;,[],536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^Hlogseq____&quot;,182,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^17logseq____&quot;,true,536870923]],[logseq____&quot;^15logseq____&quot;,[238,logseq____&quot;^;logseq____&quot;,logseq____&quot;~u65291dd2-72ce-463a-ab96-deb7dc39678blogseq____&quot;,536870923]],[logseq____&quot;^15logseq____&quot;,[239,logseq____&quot;^Qlogseq____&quot;,logseq____&quot;wobei $\\\\pi$ eine \\logseq____&quot;[[Permutation]]\\logseq____&quot; der Zahl $(1,2,\\\\cdots,n)$ 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q)\\\\land r logseq____&amp;\\\\equiv p\\\\land(q\\\\land r),\\\\quadlogseq____&amp;\\\\text{schreibe daher: } p\\\\land q\\\\land r,\\\\quad \\\\land \\\\text{ assoziativ}\\\\\\\\\\n(p \\\\lor q) \\\\lor r logseq____&amp;\\\\equiv p \\\\lor (q\\\\lor r),\\\\quadlogseq____&amp;\\\\text{schreibe daher: } p\\\\lor q\\\\lor r,\\\\quad \\\\lor \\\\text{ assoziativ}\\\\\\\\\\np \\\\land q logseq____&amp;\\\\equiv q \\\\land p,\\\\quad \\\\land logseq____&amp;\\\\text{ kommutativ}\\\\\\\\\\np \\\\lor q logseq____&amp;\\\\equiv q \\\\lor p,\\\\quad \\\\lor logseq____&amp;\\\\text{ kommutativ}\\\\\\\\\\n\\\\neg(\\\\neg p) logseq____&amp;\\\\equiv p, \\\\quad \\\\neg logseq____&amp;\\\\text{ idenpotent}\\\\\\\\\\np\\\\land(q\\\\lor r)logseq____&amp;\\\\equiv (p\\\\land q)\\\\lor(p\\\\land r);\\\\notag\\\\\\\\\\np\\\\lor(q\\\\land r)logseq____&amp;\\\\equiv (p\\\\lor q)\\\\lor(p\\\\land r),\\\\quad logseq____&amp;\\\\land,\\\\lor\\\\text{ wechselseitig distributiv}\\\\\\\\\\n\\\\neg(p\\\\land 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