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[[Rationalmachen]] des [[Nenner]]slogseq____",536870919]],[logseq____"^15logseq____",[53,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[53,logseq____"^Flogseq____",64,536870919]],[logseq____"^15logseq____",[53,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[53,logseq____"^Vlogseq____",69,536870919]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",39,536870919]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[53,logseq____"^Ulogseq____",45,536870919]],[logseq____"^15logseq____",[53,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[53,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[53,logseq____"^Hlogseq____",39,536870919]],[logseq____"^15logseq____",[53,logseq____"^Hlogseq____",45,536870919]],[logseq____"^15logseq____",[53,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[53,logseq____"^;logseq____",logseq____"~u652febdd-e905-4cc3-9da9-b4c5f9c2b0eclogseq____",536870919]],[logseq____"^15logseq____",[54,logseq____"^Qlogseq____",logseq____"#FIXME $\\\\sin^{-2}x+cos^2y=1,r$ ist falschlogseq____",536870919]],[logseq____"^15logseq____",[54,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[54,logseq____"^Flogseq____",94,536870919]],[logseq____"^15logseq____",[54,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[54,logseq____"^Vlogseq____",94,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[54,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[54,logseq____"^Hlogseq____",42,536870919]],[logseq____"^15logseq____",[54,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[54,logseq____"^;logseq____",logseq____"~u652febdd-fadf-4a79-88d3-43567380b7c3logseq____",536870919]],[logseq____"^15logseq____",[55,logseq____"^Qlogseq____",logseq____"#FIXME gleichung (50) hat angeblich noch ne Zeile $=x^0+3ylogseq____>0$ welche keinen Sinn ergibtlogseq____",536870919]],[logseq____"^15logseq____",[55,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[55,logseq____"^Flogseq____",51,536870919]],[logseq____"^15logseq____",[55,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[55,logseq____"^Vlogseq____",66,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[55,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[55,logseq____"^Hlogseq____",42,536870919]],[logseq____"^15logseq____",[55,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[55,logseq____"^;logseq____",logseq____"~u652febdd-8f84-423a-9a64-152ddbcc8b8elogseq____",536870919]],[logseq____"^15logseq____",[56,logseq____"^Qlogseq____",logseq____"$\\\\text{Die Lösung von } x^n-a=0 \\\\text{ ist } x=\\\\sqrt[n]a$ #FIXME ich glaube hier fehlt logseq____>0 constraintlogseq____",536870919]],[logseq____"^15logseq____",[56,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[56,logseq____"^Flogseq____",69,536870919]],[logseq____"^15logseq____",[56,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[56,logseq____"^Vlogseq____",69,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[56,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[56,logseq____"^Hlogseq____",42,536870919]],[logseq____"^15logseq____",[56,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[56,logseq____"^;logseq____",logseq____"~u652febdd-1d22-4232-9bd5-b090fe7dca5dlogseq____",536870919]],[logseq____"^15logseq____",[57,logseq____"^Qlogseq____",logseq____"$\\\\text{Alte Schreibweise}$\\n\\\\begin{align}\\n\\\\text{cosa }logseq____&\\\\text{plus }logseq____&\\\\text{cubus }logseq____&\\\\text{acq }logseq____&6\\\\\\\\\\nxlogseq____&+logseq____&x^3logseq____&=logseq____&6\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[57,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[57,logseq____"^Flogseq____",65,536870919]],[logseq____"^15logseq____",[57,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[57,logseq____"^Vlogseq____",72,536870919]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[57,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[57,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[57,logseq____"^;logseq____",logseq____"~u652febdd-b85d-4f6e-a294-70572b59f15alogseq____",536870919]],[logseq____"^15logseq____",[58,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870919]],[logseq____"^15logseq____",[58,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[58,logseq____"^Flogseq____",70,536870919]],[logseq____"^15logseq____",[58,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[58,logseq____"^Vlogseq____",95,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[58,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[58,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[58,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[58,logseq____"^;logseq____",logseq____"~u652febdd-a9b6-4df0-9344-641c528f0ec5logseq____",536870919]],[logseq____"^15logseq____",[59,logseq____"^Qlogseq____",logseq____"$\\\\text{Häufige Falle:}$\\n\\\\begin{align}\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=(-1)^\\\\frac22logseq____&=(-1)^1logseq____&=-1\\\\\\\\\\n\\\\left((-1)^2\\\\right)^\\\\frac12logseq____&=1^\\\\frac12logseq____&logseq____&=1\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[59,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[59,logseq____"^Flogseq____",52,536870919]],[logseq____"^15logseq____",[59,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[59,logseq____"^Vlogseq____",82,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[59,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[59,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[59,logseq____"^;logseq____",logseq____"~u652febdd-c5c4-4ecc-83be-bf444154574elogseq____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Logarithmen]]logseq____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[60,logseq____"^Flogseq____",47,536870919]],[logseq____"^15logseq____",[60,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[60,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",31,536870919]],[logseq____"^15logseq____",[60,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[60,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[60,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[60,logseq____"^Hlogseq____",31,536870919]],[logseq____"^15logseq____",[60,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[60,logseq____"^;logseq____",logseq____"~u652febdd-962e-44a8-9fbc-9569c46d6ef3logseq____",536870919]],[logseq____"^15logseq____",[61,logseq____"^Qlogseq____",logseq____"# [[Potenzen]] und [[Wurzeln]]logseq____",536870919]],[logseq____"^15logseq____",[61,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[61,logseq____"^Flogseq____",62,536870919]],[logseq____"^15logseq____",[61,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[61,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[61,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[61,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[61,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[61,logseq____"^Hlogseq____",27,536870919]],[logseq____"^15logseq____",[61,logseq____"^Hlogseq____",37,536870919]],[logseq____"^15logseq____",[61,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[61,logseq____"^;logseq____",logseq____"~u652febdd-183b-4ec4-aaf4-5e164a4bcdf2logseq____",536870919]],[logseq____"^15logseq____",[62,logseq____"^Qlogseq____",logseq____"# [[Binomische Formeln]]logseq____",536870919]],[logseq____"^15logseq____",[62,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[62,logseq____"^Flogseq____",88,536870919]],[logseq____"^15logseq____",[62,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[62,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[62,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[62,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[62,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[62,logseq____"^Hlogseq____",34,536870919]],[logseq____"^15logseq____",[62,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[62,logseq____"^;logseq____",logseq____"~u652febdd-84da-4f65-99b5-6486bc7ba7dclogseq____",536870919]],[logseq____"^15logseq____",[63,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\sqrt{a+5}-\\\\sqrt{x+3}logseq____&=2\\\\sqrt(x+1) logseq____&|logseq____&()^2\\\\\\\\\\n\\\\left(\\\\sqrt{x+5}-\\\\sqrt{x+3}\\\\right)^2logseq____&=4(x+1)\\\\\\\\\\n(x+5)-2\\\\sqrt{x+5}\\\\sqrt{x+3}+(x+3)logseq____&=4x+4logseq____&|logseq____&-(2x+8)\\\\\\\\\\n-2\\\\sqrt{(x+5)(x+3)}logseq____&=2x-4 logseq____&|logseq____&()^2\\\\\\\\\\n4(x+5)(x+3)logseq____&=4x^2-16x+16\\\\\\\\\\n4x^2+32x+60logseq____&=4x^2-16x+16logseq____&|logseq____&-4x^2+16x-16\\\\\\\\\\n48x+44logseq____&=0\\\\quad x=-\\\\frac{11}{12}\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[63,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[63,logseq____"^Flogseq____",86,536870919]],[logseq____"^15logseq____",[63,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[63,logseq____"^Vlogseq____",86,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",30,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[63,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[63,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[63,logseq____"^;logseq____",logseq____"~u652febdd-bebc-43fa-b68c-c9d362e7afe9logseq____",536870919]],[logseq____"^15logseq____",[64,logseq____"^Qlogseq____",logseq____"$\\\\text{Allgemein}$\\n\\\\begin{align}\\n|y|logseq____&=\\\\begin{cases}\\ny logseq____&\\\\text{ falls } y\\\\ge0\\\\\\\\\\n-y logseq____&\\\\text{ falls } ylogseq____<0\\\\\\\\\\n\\\\end{cases}\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[64,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[64,logseq____"^Flogseq____",66,536870919]],[logseq____"^15logseq____",[64,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[64,logseq____"^Vlogseq____",69,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[64,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[64,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[64,logseq____"^;logseq____",logseq____"~u652febdd-2be9-43b5-87e1-9e6703034112logseq____",536870919]],[logseq____"^15logseq____",[65,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870919]],[logseq____"^15logseq____",[65,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[65,logseq____"^Flogseq____",78,536870919]],[logseq____"^15logseq____",[65,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[65,logseq____"^Vlogseq____",72,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[65,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[65,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[65,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[65,logseq____"^;logseq____",logseq____"~u652febdd-6dbe-449e-958d-6a274a59bde6logseq____",536870919]],[logseq____"^15logseq____",[66,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870919]],[logseq____"^15logseq____",[66,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[66,logseq____"^Flogseq____",101,536870919]],[logseq____"^15logseq____",[66,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[66,logseq____"^Vlogseq____",69,536870919]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[66,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[66,logseq____"^Hlogseq____",35,536870919]],[logseq____"^15logseq____",[66,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[66,logseq____"^;logseq____",logseq____"~u652febdd-70a5-460a-8a7f-75353bfdef99logseq____",536870919]],[logseq____"^15logseq____",[67,logseq____"^Qlogseq____",logseq____"Das [[Pascalsche Dreieck]] lässt sich auch mit den entsprechenden Binomialkoeffizienten darstellenlogseq____",536870919]],[logseq____"^15logseq____",[67,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[67,logseq____"^Flogseq____",79,536870919]],[logseq____"^15logseq____",[67,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[67,logseq____"^Vlogseq____",79,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",32,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",38,536870919]],[logseq____"^15logseq____",[67,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[67,logseq____"^Hlogseq____",38,536870919]],[logseq____"^15logseq____",[67,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[67,logseq____"^;logseq____",logseq____"~u652febdd-128a-40c6-b2cd-07b7a086fbd6logseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Qlogseq____",logseq____"# [[Links]]logseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[68,logseq____"^Flogseq____",40,536870919]],[logseq____"^15logseq____",[68,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[68,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[68,logseq____"^Ulogseq____",44,536870919]],[logseq____"^15logseq____",[68,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[68,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[68,logseq____"^Hlogseq____",44,536870919]],[logseq____"^15logseq____",[68,logseq____"^17logseq____",false,536870919]],[logseq____"^15logseq____",[68,logseq____"^;logseq____",logseq____"~u652febdd-d255-4df0-9eae-a6070d256e67logseq____",536870919]],[logseq____"^15logseq____",[69,logseq____"^Qlogseq____",logseq____"# [[Wurzeln]]logseq____",536870919]],[logseq____"^15logseq____",[69,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[69,logseq____"^Flogseq____",72,536870919]],[logseq____"^15logseq____",[69,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[69,logseq____"^Vlogseq____",61,536870919]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[69,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[69,logseq____"^?logseq____",[logseq____"^ 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3}\\n\\\\\\\\\\n\\\\cdots\\n\\\\end{array}logseq____",536870919]],[logseq____"^15logseq____",[83,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[83,logseq____"^Flogseq____",67,536870919]],[logseq____"^15logseq____",[83,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[83,logseq____"^Vlogseq____",79,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",32,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[83,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[83,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[83,logseq____"^;logseq____",logseq____"~u652febdd-332e-4883-851b-a8d7ecd807bdlogseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Qlogseq____",logseq____"$\\\\text{Herleitung mit }$[[Quadratische Ergänzung]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&=0logseq____&|logseq____&-q\\\\\\\\\\nx^2+pxlogseq____&=-qlogseq____&|logseq____&+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\nx^2+px+\\\\left(\\\\frac p2\\\\right)^2logseq____&=-q+\\\\left(\\\\frac p2\\\\right)^2\\\\\\\\\\n\\\\underbrace{\\\\left(x+\\\\frac p2\\\\right)^2}_\\\\text{1. binomische Formel}logseq____&=-q+\\\\left(\\\\frac p2\\\\right)^2logseq____&|logseq____&\\\\sqrt{()}\\\\\\\\\\n\\\\left|x+\\\\frac p2\\\\right|logseq____&=\\\\sqrt{\\\\frac{p^2}4-q}logseq____&,logseq____&\\\\text{ falls }\\\\frac{p^2}4-q\\\\ge0\\\\\\\\\\nx+\\\\frac p2logseq____&=\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}logseq____&|logseq____&-\\\\frac p2\\\\\\\\\\nxlogseq____&=-\\\\frac p2\\\\pm\\\\sqrt{\\\\frac{p^2}4-q}\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[84,logseq____"^Flogseq____",97,536870919]],[logseq____"^15logseq____",[84,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[84,logseq____"^Vlogseq____",97,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",26,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[84,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[84,logseq____"^Hlogseq____",26,536870919]],[logseq____"^15logseq____",[84,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[84,logseq____"^;logseq____",logseq____"~u652febdd-707d-4018-b715-43e36543c797logseq____",536870919]],[logseq____"^15logseq____",[85,logseq____"^Qlogseq____",logseq____"[[Wolframalpha]]logseq____",536870919]],[logseq____"^15logseq____",[85,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[85,logseq____"^Flogseq____",68,536870919]],[logseq____"^15logseq____",[85,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[85,logseq____"^Vlogseq____",68,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",44,536870919]],[logseq____"^15logseq____",[85,logseq____"^Ulogseq____",46,536870919]],[logseq____"^15logseq____",[85,logseq____"^Hlogseq____",46,536870919]],[logseq____"^15logseq____",[85,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[85,logseq____"^;logseq____",logseq____"~u652febdd-9869-46b3-b75e-5165609dc3ealogseq____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Qlogseq____",logseq____"# [[Wurzelgleichung]]logseq____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[86,logseq____"^Flogseq____",73,536870919]],[logseq____"^15logseq____",[86,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[86,logseq____"^Vlogseq____",61,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",30,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[86,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[86,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[86,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[86,logseq____"^Hlogseq____",30,536870919]],[logseq____"^15logseq____",[86,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[86,logseq____"^;logseq____",logseq____"~u652febdd-1d7b-48ab-8a26-9a2ade6c957blogseq____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n$\\\\text{Wenn } 10^x=y \\\\text{, dann}$\\n\\\\begin{align}\\nxlogseq____&=\\\\lg y logseq____& ,r\\\\\\\\\\nxlogseq____&=\\\\log_y10logseq____&,f\\\\\\\\\\nxlogseq____&=\\\\log_{10}ylogseq____&,r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&= \\\\ln 2 logseq____&, r \\\\\\\\\\n\\\\ln 4 - \\\\ln 2 logseq____&= \\\\ln 8 logseq____&, f \\\\\\\\\\n\\\\ln 4 + \\\\ln 2 logseq____&= \\\\ln 8 logseq____&, r \\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[87,logseq____"^Flogseq____",60,536870919]],[logseq____"^15logseq____",[87,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[87,logseq____"^Vlogseq____",60,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",31,536870919]],[logseq____"^15logseq____",[87,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[87,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[87,logseq____"^;logseq____",logseq____"~u652febdd-3087-485e-bc99-24d006b22e5elogseq____",536870919]],[logseq____"^15logseq____",[88,logseq____"^Qlogseq____",logseq____"# Wissensabgleich [[Trigonometrie]]logseq____",536870919]],[logseq____"^15logseq____",[88,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[88,logseq____"^Flogseq____",49,536870919]],[logseq____"^15logseq____",[88,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[88,logseq____"^Vlogseq____",40,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[88,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[88,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870919]],[logseq____"^15logseq____",[88,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[88,logseq____"^Hlogseq____",36,536870919]],[logseq____"^15logseq____",[88,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[88,logseq____"^;logseq____",logseq____"~u652febdd-b565-46eb-bd48-c36c3b19c067logseq____",536870919]],[logseq____"^15logseq____",[89,logseq____"^Qlogseq____",logseq____"https://www.wolframalpha.comlogseq____",536870919]],[logseq____"^15logseq____",[89,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[89,logseq____"^Flogseq____",85,536870919]],[logseq____"^15logseq____",[89,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[89,logseq____"^Vlogseq____",85,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",44,536870919]],[logseq____"^15logseq____",[89,logseq____"^Ulogseq____",46,536870919]],[logseq____"^15logseq____",[89,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[89,logseq____"^;logseq____",logseq____"~u652febdd-9d6d-4113-a29f-69dd2677ba5dlogseq____",536870919]],[logseq____"^15logseq____",[90,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiel für die 3. Binomische Formel}$\\n\\\\begin{align}\\n\\\\frac{\\\\frac1{a-b}+\\\\frac1{a+b}}{\\\\frac1{a-b}-\\\\frac1{a+b}}\\nlogseq____&=\\\\frac{\\\\frac{a+b+a-b}{(a+b)*(a-b)}}{\\\\frac{a+b-(a-b)}{(a+b)*(a-b)}}\\nlogseq____&=\\\\frac{a+b+a-b}{a+b-a+b}\\nlogseq____&=\\\\frac{2a}{2b}\\nlogseq____&=\\\\frac ab\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[90,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[90,logseq____"^Flogseq____",104,536870919]],[logseq____"^15logseq____",[90,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[90,logseq____"^Vlogseq____",62,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[90,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[90,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[90,logseq____"^;logseq____",logseq____"~u652febdd-a76f-4d18-8986-161b5a556977logseq____",536870919]],[logseq____"^15logseq____",[91,logseq____"^Qlogseq____",logseq____"[[Satz von Vieta]]\\n\\\\begin{align}\\nx^2+px+qlogseq____&=0 logseq____&logseq____& \\\\text{habe }x_{1,2}\\\\text{ als Lösung}\\\\\\\\\\nx_1+x_2logseq____&=-p logseq____&logseq____& x_1*x_2=q\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[91,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[91,logseq____"^Flogseq____",84,536870919]],[logseq____"^15logseq____",[91,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[91,logseq____"^Vlogseq____",97,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",41,536870919]],[logseq____"^15logseq____",[91,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[91,logseq____"^Hlogseq____",41,536870919]],[logseq____"^15logseq____",[91,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[91,logseq____"^;logseq____",logseq____"~u652febdd-dc08-41af-b5b5-9740124cead1logseq____",536870919]],[logseq____"^15logseq____",[92,logseq____"^Qlogseq____",logseq____"Einsetzen, um zu überprüfen, ob man eine Fallunterscheidung brauchtlogseq____",536870919]],[logseq____"^15logseq____",[92,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[92,logseq____"^Flogseq____",63,536870919]],[logseq____"^15logseq____",[92,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[92,logseq____"^Vlogseq____",86,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",30,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[92,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[92,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[92,logseq____"^;logseq____",logseq____"~u652febdd-c670-4624-ac65-8f661f0ffeddlogseq____",536870919]],[logseq____"^15logseq____",[93,logseq____"^Qlogseq____",logseq____"#FIXME $(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5=2+20x+40x^2$ ist Falschlogseq____",536870919]],[logseq____"^15logseq____",[93,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[93,logseq____"^Flogseq____",96,536870919]],[logseq____"^15logseq____",[93,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[93,logseq____"^Vlogseq____",58,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[93,logseq____"^Ulogseq____",42,536870919]],[logseq____"^15logseq____",[93,logseq____"^Hlogseq____",42,536870919]],[logseq____"^15logseq____",[93,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[93,logseq____"^;logseq____",logseq____"~u652febdd-635b-4ca0-a367-29ef3a312978logseq____",536870919]],[logseq____"^15logseq____",[94,logseq____"^Qlogseq____",logseq____"$\\\\text{Welche Gleichungen sind richtig?}$\\n\\\\begin{align}\\n\\\\tan x logseq____&= \\\\frac{\\\\sin x}{\\\\cos x} logseq____&, \\\\cos x \\\\ne 0\\\\\\\\\\n\\\\sin^{-2}x-\\\\cos^2xlogseq____&=1logseq____&,f\\\\\\\\\\n\\\\sin x = \\\\cos x logseq____&= 1 logseq____&, f\\\\\\\\\\n\\\\sin^{-2}x+cos^2ylogseq____&=1logseq____&,r\\\\\\\\\\n1+tan^2xlogseq____&=\\\\frac1{\\\\cos^2x}logseq____&,\\\\cos x\\\\ne0\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[94,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[94,logseq____"^Flogseq____",76,536870919]],[logseq____"^15logseq____",[94,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[94,logseq____"^Vlogseq____",88,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",36,536870919]],[logseq____"^15logseq____",[94,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[94,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[94,logseq____"^;logseq____",logseq____"~u652febdd-0afa-4df3-bc5f-80a88f5fa656logseq____",536870919]],[logseq____"^15logseq____",[95,logseq____"^Qlogseq____",logseq____"## [[Pascalsches Dreieck]]logseq____",536870919]],[logseq____"^15logseq____",[95,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[95,logseq____"^Flogseq____",90,536870919]],[logseq____"^15logseq____",[95,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[95,logseq____"^Vlogseq____",62,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[95,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[95,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[95,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[95,logseq____"^Hlogseq____",28,536870919]],[logseq____"^15logseq____",[95,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[95,logseq____"^;logseq____",logseq____"~u652febdd-54d9-4e6e-8bb0-b85b0bb7ca12logseq____",536870919]],[logseq____"^15logseq____",[96,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n(2x+y)^4logseq____&=(2x)^4+4*(2x)^3y+6*(2x)^2y^2+4*2xy^3+y^4\\\\notag\\\\\\\\\\nlogseq____&=16x^4+32x^3y+24x^2y^2+8xy^3+y^4\\\\\\\\\\n(1+\\\\sqrt x)^5*(1-\\\\sqrt x)^5logseq____&=2+20x+40x^2\\\\\\\\\\n\\\\end{align}logseq____",536870919]],[logseq____"^15logseq____",[96,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[96,logseq____"^Flogseq____",58,536870919]],[logseq____"^15logseq____",[96,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[96,logseq____"^Vlogseq____",58,536870919]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",28,536870919]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",34,536870919]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",35,536870919]],[logseq____"^15logseq____",[96,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[96,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[96,logseq____"^;logseq____",logseq____"~u652febdd-9a9e-4e26-8974-0ca401ede372logseq____",536870919]],[logseq____"^15logseq____",[97,logseq____"^Qlogseq____",logseq____"## [[pq-Formel]]logseq____",536870919]],[logseq____"^15logseq____",[97,logseq____"^Ologseq____",logseq____"^16logseq____",536870919]],[logseq____"^15logseq____",[97,logseq____"^Flogseq____",98,536870919]],[logseq____"^15logseq____",[97,logseq____"^Xlogseq____",40,536870919]],[logseq____"^15logseq____",[97,logseq____"^Vlogseq____",73,536870919]],[logseq____"^15logseq____",[97,logseq____"^Ulogseq____",27,536870919]],[logseq____"^15logseq____",[97,logseq____"^Ulogseq____",29,536870919]],[logseq____"^15logseq____",[97,logseq____"^Ulogseq____",37,536870919]],[logseq____"^15logseq____",[97,logseq____"^Ulogseq____",40,536870919]],[logseq____"^15logseq____",[97,logseq____"^Ulogseq____",43,536870919]],[logseq____"^15logseq____",[97,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870919]],[logseq____"^15logseq____",[97,logseq____"^Jlogseq____",[],536870919]],[logseq____"^15logseq____",[97,logseq____"^Hlogseq____",43,536870919]],[logseq____"^15logseq____",[97,logseq____"^17logseq____",true,536870919]],[logseq____"^15logseq____",[97,logseq____"^;logseq____",logseq____"~u652febdd-8d47-49f3-a355-1404b14f83eelogseq____",536870919]],[logseq____"^15logseq____",[98,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nax^2+bx+clogseq____&=0logseq____&|:a\\\\quadlogseq____&a\\\\ne0\\\\\\\\\\nx^2+\\\\frac ba x + \\\\frac ca logseq____&= 0\\\\\\\\\\nplogseq____&=\\\\frac ba,logseq____&q = \\\\frac 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[[Lösungsmengen]]logseq____",536870920]],[logseq____"^15logseq____",[119,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[119,logseq____"^Flogseq____",147,536870920]],[logseq____"^15logseq____",[119,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[119,logseq____"^Vlogseq____",160,536870920]],[logseq____"^15logseq____",[119,logseq____"^Ulogseq____",111,536870920]],[logseq____"^15logseq____",[119,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[119,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[119,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870920]],[logseq____"^15logseq____",[119,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[119,logseq____"^Hlogseq____",111,536870920]],[logseq____"^15logseq____",[119,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[119,logseq____"^;logseq____",logseq____"~u652febdd-94b9-4ca0-b439-748c8982e110logseq____",536870920]],[logseq____"^15logseq____",[120,logseq____"^Qlogseq____",logseq____"Kombinieren:\\n\\\\begin{align}\\nL=L_1\\\\cup L_2=[3,\\\\infty)\\\\cup\\\\left[\\\\frac12,3\\\\right)=\\\\left[\\\\frac12,\\\\infty\\\\right)\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[120,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[120,logseq____"^Flogseq____",124,536870920]],[logseq____"^15logseq____",[120,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[120,logseq____"^Vlogseq____",153,536870920]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",108,536870920]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",113,536870920]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",115,536870920]],[logseq____"^15logseq____",[120,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[120,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[120,logseq____"^;logseq____",logseq____"~u652febdd-e90f-4c26-add4-dd30e06318b2logseq____",536870920]],[logseq____"^15logseq____",[121,logseq____"^Qlogseq____",logseq____"**oder** $\\\\rightarrow$ 5 ist abstand von x zu 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incompletelogseq____",536870920]],[logseq____"^15logseq____",[122,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[122,logseq____"^Flogseq____",160,536870920]],[logseq____"^15logseq____",[122,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[122,logseq____"^Vlogseq____",114,536870920]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",42,536870920]],[logseq____"^15logseq____",[122,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[122,logseq____"^Hlogseq____",42,536870920]],[logseq____"^15logseq____",[122,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[122,logseq____"^;logseq____",logseq____"~u652febdd-1046-4c2c-93da-083d1f80e232logseq____",536870920]],[logseq____"^15logseq____",[123,logseq____"^Qlogseq____",logseq____"$$L=\\\\left\\\\{\\\\underbrace{x\\\\in\\\\Reals}_{0\\\\notin L}\\\\:\\\\middle|\\\\:\\\\underbrace{|x-3|\\\\le|x+2}_{1\\\\in L}\\\\right\\\\}$$\\n$0\\\\notin L\\\\rightarrow\\\\text{0 steht nicht in Lösungsmenge}$\\n$1\\\\in L\\\\rightarrow\\\\text{1 gehört zu 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2b}\\\\quad xlogseq____<-2$\\n\\\\begin{align}\\n|\\\\underbrace{x+2}_{logseq____<0}logseq____&=-(x+2)=-x-2\\\\\\\\\\n-x+3logseq____&\\\\le -x-2 logseq____&|logseq____&+x\\\\\\\\\\n3logseq____&\\\\le-2logseq____&logseq____&\\\\underset{falsche 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aller rellen Zahlen zwischen 4 und $\\\\infty$ ohne 4 und $\\\\infty$\\n\\\\begin{align}\\\\left\\\\{x\\\\in\\\\Reals\\\\middle|xlogseq____>4\\\\right\\\\}=:(4,\\\\infty)\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[125,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[125,logseq____"^Flogseq____",156,536870920]],[logseq____"^15logseq____",[125,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[125,logseq____"^Vlogseq____",143,536870920]],[logseq____"^15logseq____",[125,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[125,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[125,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[125,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[125,logseq____"^;logseq____",logseq____"~u652febdd-87c7-4607-b7cf-0b9d90ab03c5logseq____",536870920]],[logseq____"^15logseq____",[126,logseq____"^Qlogseq____",logseq____"$\\\\text{Fall 2}\\\\quad x\\\\ge3$\\n\\\\begin{align}\\n|x-3|logseq____&=-x+3\\\\\\\\\\nx-3logseq____&logseq____<5 logseq____&|logseq____&+3\\\\\\\\\\nxlogseq____&logseq____<8\\\\\\\\\\nL_2logseq____&=[3,8)\\\\\\\\\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[126,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[126,logseq____"^Flogseq____",159,536870920]],[logseq____"^15logseq____",[126,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[126,logseq____"^Vlogseq____",129,536870920]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",108,536870920]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",113,536870920]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",115,536870920]],[logseq____"^15logseq____",[126,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[126,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[126,logseq____"^;logseq____",logseq____"~u652febdd-4858-4ade-a23c-fef0cf7a5b12logseq____",536870920]],[logseq____"^15logseq____",[127,logseq____"^Qlogseq____",logseq____"Kombinieren:\\n\\\\begin{align}\\nL=L_1\\\\cup 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logseq____",logseq____"^18logseq____",3],536870920]],[logseq____"^15logseq____",[128,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[128,logseq____"^Hlogseq____",108,536870920]],[logseq____"^15logseq____",[128,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[128,logseq____"^;logseq____",logseq____"~u652febdd-4e61-49eb-82c9-1fb490d10378logseq____",536870920]],[logseq____"^15logseq____",[129,logseq____"^Qlogseq____",logseq____"### Lösung mit [[Fallunterscheidung]]logseq____",536870920]],[logseq____"^15logseq____",[129,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[129,logseq____"^Flogseq____",131,536870920]],[logseq____"^15logseq____",[129,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[129,logseq____"^Vlogseq____",131,536870920]],[logseq____"^15logseq____",[129,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[129,logseq____"^Ulogseq____",108,536870920]],[logseq____"^15logseq____",[129,logseq____"^Ulogseq____",113,536870920]],[logseq____"^15logseq____",[129,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[129,logseq____"^Ulogseq____",115,536870920]],[logseq____"^15logseq____",[129,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[129,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870920]],[logseq____"^15logseq____",[129,logseq____"^Jlogseq____",[],536870920]],[logseq____"^15logseq____",[129,logseq____"^Hlogseq____",108,536870920]],[logseq____"^15logseq____",[129,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[129,logseq____"^;logseq____",logseq____"~u652febdd-3bf8-4ddc-b7dc-f9a5e67962a6logseq____",536870920]],[logseq____"^15logseq____",[130,logseq____"^Qlogseq____",logseq____"[Menge]([[Mengen]]) von [Punkten]([[Punkte]]) $(x,y)$ in der [Ebene]([[Ebenen]]) die den gleichen [[Abstand]] r ([[Radius]]) zu einem festen [Punkt]([[Punkte]]) ([[Mittelpunkt]])logseq____",536870920]],[logseq____"^15logseq____",[130,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[130,logseq____"^Flogseq____",141,536870920]],[logseq____"^15logseq____",[130,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[130,logseq____"^Vlogseq____",141,536870920]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",106,536870920]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",107,536870920]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",109,536870920]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",112,536870920]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",116,536870920]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",117,536870920]],[logseq____"^15logseq____",[130,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[130,logseq____"^Hlogseq____",107,536870920]],[logseq____"^15logseq____",[130,logseq____"^Hlogseq____",109,536870920]],[logseq____"^15logseq____",[130,logseq____"^Hlogseq____",112,536870920]],[logseq____"^15logseq____",[130,logseq____"^Hlogseq____",116,536870920]],[logseq____"^15logseq____",[130,logseq____"^Hlogseq____",117,536870920]],[logseq____"^15logseq____",[130,logseq____"^Hlogseq____",118,536870920]],[logseq____"^15logseq____",[130,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[130,logseq____"^;logseq____",logseq____"~u652febdd-98c0-4e6d-9342-11789fd03869logseq____",536870920]],[logseq____"^15logseq____",[131,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nLlogseq____&=\\\\left\\\\{x\\\\in\\\\Reals\\\\Big||x-3|logseq____<5\\\\right\\\\}=(-2,8)\\n\\\\end{align}logseq____",536870920]],[logseq____"^15logseq____",[131,logseq____"^Ologseq____",logseq____"^16logseq____",536870920]],[logseq____"^15logseq____",[131,logseq____"^Flogseq____",144,536870920]],[logseq____"^15logseq____",[131,logseq____"^Xlogseq____",114,536870920]],[logseq____"^15logseq____",[131,logseq____"^Vlogseq____",157,536870920]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",35,536870920]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",113,536870920]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",114,536870920]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",115,536870920]],[logseq____"^15logseq____",[131,logseq____"^Ulogseq____",118,536870920]],[logseq____"^15logseq____",[131,logseq____"^17logseq____",true,536870920]],[logseq____"^15logseq____",[131,logseq____"^;logseq____",logseq____"~u652febdd-eedf-45aa-80d9-c31f0cd6b729logseq____",536870920]],[logseq____"^15logseq____",[132,logseq____"^Qlogseq____",logseq____"$(x_M,y_M)$ 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x\\\\ge-2$\\n\\\\begin{align}\\n|\\\\underbrace{x+2}_{\\\\ge0}logseq____&=x+2\\\\\\\\\\n-x+3logseq____&\\\\le x+2 logseq____&|logseq____& -2\\\\\\\\\\n-x+1logseq____&\\\\le x logseq____&|logseq____& +x\\\\\\\\\\n\\\\frac12logseq____&\\\\le x logseq____&|logseq____& 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q$|\\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____",536870922]],[logseq____"^15logseq____",[188,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[188,logseq____"^Flogseq____",198,536870922]],[logseq____"^15logseq____",[188,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[188,logseq____"^Vlogseq____",209,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",168,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",182,536870922]],[logseq____"^15logseq____",[188,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[188,logseq____"^Hlogseq____",168,536870922]],[logseq____"^15logseq____",[188,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[188,logseq____"^;logseq____",logseq____"~u652febdd-3f9b-4892-8f7f-8169b3b3b347logseq____",536870922]],[logseq____"^15logseq____",[189,logseq____"^Qlogseq____",logseq____"Sind $p$ und $q$ [[Aussagen]], so auch\\n\\\\begin{align}\\n(p\\\\land q) logseq____&\\\\quadlogseq____& (\\logseq____"\\\\text{und}\\logseq____")\\\\\\\\\\n(p\\\\lor q) logseq____&logseq____& (\\logseq____"\\\\text{oder}\\logseq____")\\\\\\\\\\n(\\\\neg p) logseq____&logseq____& (\\logseq____"\\\\text{nicht}\\logseq____")\\\\\\\\\\n(p\\\\rightarrow q) logseq____&logseq____& (\\logseq____"\\\\text{impliziert}\\logseq____")\\\\\\\\\\n(p\\\\leftrightarrow q) logseq____&logseq____& (\\logseq____"\\\\text{genau dann wenn}\\logseq____")\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[189,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[189,logseq____"^Flogseq____",207,536870922]],[logseq____"^15logseq____",[189,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[189,logseq____"^Vlogseq____",207,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[189,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[189,logseq____"^Hlogseq____",180,536870922]],[logseq____"^15logseq____",[189,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[189,logseq____"^;logseq____",logseq____"~u652febdd-7bd7-4b96-b6ee-bb2e459bd021logseq____",536870922]],[logseq____"^15logseq____",[190,logseq____"^Qlogseq____",logseq____"Formel, die konstant $w$ istlogseq____",536870922]],[logseq____"^15logseq____",[190,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[190,logseq____"^Flogseq____",212,536870922]],[logseq____"^15logseq____",[190,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[190,logseq____"^Vlogseq____",212,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[190,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[190,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[190,logseq____"^;logseq____",logseq____"~u652febdd-4e11-4827-a533-81f1c6a86d56logseq____",536870922]],[logseq____"^15logseq____",[191,logseq____"^Qlogseq____",logseq____"Formel, die konstant $f$ istlogseq____",536870922]],[logseq____"^15logseq____",[191,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[191,logseq____"^Flogseq____",195,536870922]],[logseq____"^15logseq____",[191,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[191,logseq____"^Vlogseq____",195,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",175,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[191,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[191,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[191,logseq____"^;logseq____",logseq____"~u652febdd-4679-4c80-80bd-b80da129866clogseq____",536870922]],[logseq____"^15logseq____",[192,logseq____"^Qlogseq____",logseq____"$\\\\text{Beispiele}$\\n\\\\begin{align}\\nlogseq____&\\logseq____"5\\\\text{ ist prim}\\logseq____" logseq____&\\\\quadlogseq____& (w)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"4\\\\text{ ist prim}\\logseq____" logseq____&logseq____& (f)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Jede gerade Zahl }\\\\ge4\\\\notag\\\\\\\\\\nlogseq____&\\\\text{ ist Summe zweier Primzahlen}\\logseq____" logseq____&logseq____& (\\\\text{Aussage, }w\\\\text{ oder }f)\\\\notag\\\\\\\\\\nlogseq____&(\\\\text{Vermutung von Goldback 1742})\\\\text{, }logseq____&logseq____&\\\\text{richtig für gerade Zahlen bis }4*10^{18}\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Dieser Satz ist falsch}\\logseq____" logseq____&logseq____& (\\\\text{keine Aussage})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Die Gleichung } x^2+y^2=z^2 \\\\notag\\\\\\\\\\nlogseq____&\\\\text{ hat eine Lösung }x,y,z\\\\notag\\\\\\\\\\nlogseq____&\\\\text{ aus positiven ganzen Zahlen}\\logseq____" logseq____&logseq____& (w\\\\text{, z.B. }x=3,y=4,z=5)\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Für }n\\\\ge3\\\\text{ hat die Gleichung }\\\\notag\\\\\\\\\\nlogseq____&x^n+y^n=z^n\\\\text{ eine Lösung}logseq____&logseq____& (f\\\\text{, wie von Fermat 1640 vermutet}\\\\notag\\\\\\\\\\nlogseq____&x,y,z \\\\text{aus positiven ganzen Zahlen}\\logseq____" logseq____&logseq____&\\\\text{und von Wiles 1994 bewiesen})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Gott ist tot}\\logseq____" logseq____&logseq____& (\\\\text{Aussage? Wohl kaum?})\\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Nietzsche ist tot}\\logseq____" logseq____&logseq____& (\\\\text{Aussage?}) \\\\\\\\\\n\\\\notag\\\\\\\\\\nlogseq____&\\logseq____"\\\\text{Die Länder einer Landkarte lassen sich}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{so mit nur vier Farben färben,}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{dass Länder mit einer gemeinsamen}\\\\notag\\\\\\\\\\nlogseq____&\\\\text{Grenzlienie verschieden gefärbt sind.}\\logseq____" logseq____&logseq____& (\\\\text{Aussagge; }w\\\\text{, sog 4-Farben-Satz})\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[192,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[192,logseq____"^Flogseq____",213,536870922]],[logseq____"^15logseq____",[192,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[192,logseq____"^Vlogseq____",202,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[192,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[192,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[192,logseq____"^;logseq____",logseq____"~u652febdd-903c-45b5-9629-0c85ea2c590dlogseq____",536870922]],[logseq____"^15logseq____",[193,logseq____"^Qlogseq____",logseq____"### [[Aussageformel]]logseq____",536870922]],[logseq____"^15logseq____",[193,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[193,logseq____"^Flogseq____",200,536870922]],[logseq____"^15logseq____",[193,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[193,logseq____"^Vlogseq____",207,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",182,536870922]],[logseq____"^15logseq____",[193,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[193,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[193,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[193,logseq____"^Hlogseq____",182,536870922]],[logseq____"^15logseq____",[193,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[193,logseq____"^;logseq____",logseq____"~u652febdd-9efa-4096-a2fa-3552dc3f708elogseq____",536870922]],[logseq____"^15logseq____",[194,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\np\\\\land q\\\\lor r\\\\\\\\\\n(p\\\\land q)\\\\lor r\\\\\\\\\\np\\\\land (q\\\\lor r)\\\\\\\\\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[194,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[194,logseq____"^Flogseq____",204,536870922]],[logseq____"^15logseq____",[194,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[194,logseq____"^Vlogseq____",204,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",35,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[194,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[194,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[194,logseq____"^;logseq____",logseq____"~u652febdd-8fec-483a-889c-4e101cb9ec19logseq____",536870922]],[logseq____"^15logseq____",[195,logseq____"^Qlogseq____",logseq____"### [[Kontradiktion]]logseq____",536870922]],[logseq____"^15logseq____",[195,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[195,logseq____"^Flogseq____",212,536870922]],[logseq____"^15logseq____",[195,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[195,logseq____"^Vlogseq____",207,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",175,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[195,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[195,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[195,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[195,logseq____"^Hlogseq____",175,536870922]],[logseq____"^15logseq____",[195,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[195,logseq____"^;logseq____",logseq____"~u652febdd-788c-4fcd-8699-144e9b676257logseq____",536870922]],[logseq____"^15logseq____",[196,logseq____"^Qlogseq____",logseq____"### [[Belegung]] (der [[Variablen]])logseq____",536870922]],[logseq____"^15logseq____",[196,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[196,logseq____"^Flogseq____",193,536870922]],[logseq____"^15logseq____",[196,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[196,logseq____"^Vlogseq____",207,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[196,logseq____"^Ulogseq____",186,536870922]],[logseq____"^15logseq____",[196,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[196,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[196,logseq____"^Hlogseq____",176,536870922]],[logseq____"^15logseq____",[196,logseq____"^Hlogseq____",186,536870922]],[logseq____"^15logseq____",[196,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[196,logseq____"^;logseq____",logseq____"~u652febdd-4cd3-4138-b2aa-891ccdb6ea98logseq____",536870922]],[logseq____"^15logseq____",[197,logseq____"^Qlogseq____",logseq____"Weitere [[Beispiele]]logseq____",536870922]],[logseq____"^15logseq____",[197,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[197,logseq____"^Flogseq____",208,536870922]],[logseq____"^15logseq____",[197,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[197,logseq____"^Vlogseq____",207,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",35,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[197,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[197,logseq____"^Hlogseq____",35,536870922]],[logseq____"^15logseq____",[197,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[197,logseq____"^;logseq____",logseq____"~u652febdd-198e-460e-ae1e-ea8e8f120643logseq____",536870922]],[logseq____"^15logseq____",[198,logseq____"^Qlogseq____",logseq____"Jede mögliche [[Belegung]] wird ein [[Wahrheitswert]] der [[Formel]] zugeordnet (nach [[Tabellenregeln]])logseq____",536870922]],[logseq____"^15logseq____",[198,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[198,logseq____"^Flogseq____",209,536870922]],[logseq____"^15logseq____",[198,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[198,logseq____"^Vlogseq____",209,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",168,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",171,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",172,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",179,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",182,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[198,logseq____"^Ulogseq____",186,536870922]],[logseq____"^15logseq____",[198,logseq____"^Hlogseq____",171,536870922]],[logseq____"^15logseq____",[198,logseq____"^Hlogseq____",172,536870922]],[logseq____"^15logseq____",[198,logseq____"^Hlogseq____",179,536870922]],[logseq____"^15logseq____",[198,logseq____"^Hlogseq____",186,536870922]],[logseq____"^15logseq____",[198,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[198,logseq____"^;logseq____",logseq____"~u652febdd-bf7e-43f7-935a-b6259af774e0logseq____",536870922]],[logseq____"^15logseq____",[199,logseq____"^Qlogseq____",logseq____"Entsteht durch sukzessive [[Verknüpfungen]] wie oben an Variablen ergibt #FIXMElogseq____",536870922]],[logseq____"^15logseq____",[199,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[199,logseq____"^Flogseq____",193,536870922]],[logseq____"^15logseq____",[199,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[199,logseq____"^Vlogseq____",193,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",42,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",181,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",182,536870922]],[logseq____"^15logseq____",[199,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[199,logseq____"^Hlogseq____",42,536870922]],[logseq____"^15logseq____",[199,logseq____"^Hlogseq____",181,536870922]],[logseq____"^15logseq____",[199,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[199,logseq____"^;logseq____",logseq____"~u652febdd-99f5-45cc-942c-0f55d0304eb8logseq____",536870922]],[logseq____"^15logseq____",[200,logseq____"^Qlogseq____",logseq____"### [[Aussagenlogische Variable]]logseq____",536870922]],[logseq____"^15logseq____",[200,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[200,logseq____"^Flogseq____",201,536870922]],[logseq____"^15logseq____",[200,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[200,logseq____"^Vlogseq____",207,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",169,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[200,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[200,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[200,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[200,logseq____"^Hlogseq____",169,536870922]],[logseq____"^15logseq____",[200,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[200,logseq____"^;logseq____",logseq____"~u652febdd-b7dc-432f-ad78-3318c6e7db24logseq____",536870922]],[logseq____"^15logseq____",[201,logseq____"^Qlogseq____",logseq____"Soweit die \\logseq____"[[Syntax]]\\logseq____", 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____",536870922]],[logseq____"^15logseq____",[201,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[201,logseq____"^Flogseq____",204,536870922]],[logseq____"^15logseq____",[201,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[201,logseq____"^Vlogseq____",207,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",172,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",177,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",179,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",183,536870922]],[logseq____"^15logseq____",[201,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[201,logseq____"^Hlogseq____",172,536870922]],[logseq____"^15logseq____",[201,logseq____"^Hlogseq____",177,536870922]],[logseq____"^15logseq____",[201,logseq____"^Hlogseq____",179,536870922]],[logseq____"^15logseq____",[201,logseq____"^Hlogseq____",183,536870922]],[logseq____"^15logseq____",[201,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[201,logseq____"^;logseq____",logseq____"~u652febdd-5fac-4924-8b01-8b2ed3ff1ee3logseq____",536870922]],[logseq____"^15logseq____",[202,logseq____"^Qlogseq____",logseq____"# 1. [[Aussagen]]logseq____",536870922]],[logseq____"^15logseq____",[202,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[202,logseq____"^Flogseq____",203,536870922]],[logseq____"^15logseq____",[202,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[202,logseq____"^Vlogseq____",165,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[202,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[202,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870922]],[logseq____"^15logseq____",[202,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[202,logseq____"^Hlogseq____",180,536870922]],[logseq____"^15logseq____",[202,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[202,logseq____"^;logseq____",logseq____"~u652febdd-9d43-4082-ac6e-3f94abf59faclogseq____",536870922]],[logseq____"^15logseq____",[203,logseq____"^Qlogseq____",logseq____"# Büchertiplogseq____",536870922]],[logseq____"^15logseq____",[203,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[203,logseq____"^Flogseq____",165,536870922]],[logseq____"^15logseq____",[203,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[203,logseq____"^Vlogseq____",165,536870922]],[logseq____"^15logseq____",[203,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[203,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870922]],[logseq____"^15logseq____",[203,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[203,logseq____"^17logseq____",false,536870922]],[logseq____"^15logseq____",[203,logseq____"^;logseq____",logseq____"~u652febdd-ca0f-42d0-bc4e-61bba9dede1blogseq____",536870922]],[logseq____"^15logseq____",[204,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870922]],[logseq____"^15logseq____",[204,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[204,logseq____"^Flogseq____",189,536870922]],[logseq____"^15logseq____",[204,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[204,logseq____"^Vlogseq____",207,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",35,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[204,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[204,logseq____"^Hlogseq____",35,536870922]],[logseq____"^15logseq____",[204,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[204,logseq____"^;logseq____",logseq____"~u652febdd-9d8c-4d4f-b852-8c31e5098edalogseq____",536870922]],[logseq____"^15logseq____",[205,logseq____"^Qlogseq____",logseq____"Zuordnung von $w/f$ an jede [Variable]([[Variablen]]) einer [[Aussageformel]]logseq____",536870922]],[logseq____"^15logseq____",[205,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[205,logseq____"^Flogseq____",196,536870922]],[logseq____"^15logseq____",[205,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[205,logseq____"^Vlogseq____",196,536870922]],[logseq____"^15logseq____",[205,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[205,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[205,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[205,logseq____"^Ulogseq____",182,536870922]],[logseq____"^15logseq____",[205,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[205,logseq____"^Ulogseq____",186,536870922]],[logseq____"^15logseq____",[205,logseq____"^Hlogseq____",176,536870922]],[logseq____"^15logseq____",[205,logseq____"^Hlogseq____",182,536870922]],[logseq____"^15logseq____",[205,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[205,logseq____"^;logseq____",logseq____"~u652febdd-9e30-43bd-8e79-551ff7f2f6celogseq____",536870922]],[logseq____"^15logseq____",[206,logseq____"^Qlogseq____",logseq____"[[Wikipedia]]logseq____",536870922]],[logseq____"^15logseq____",[206,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[206,logseq____"^Flogseq____",187,536870922]],[logseq____"^15logseq____",[206,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[206,logseq____"^Vlogseq____",203,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[206,logseq____"^Ulogseq____",170,536870922]],[logseq____"^15logseq____",[206,logseq____"^Hlogseq____",170,536870922]],[logseq____"^15logseq____",[206,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[206,logseq____"^;logseq____",logseq____"~u652febdd-a2d9-4a11-ae6a-56295dac329clogseq____",536870922]],[logseq____"^15logseq____",[207,logseq____"^Qlogseq____",logseq____"## [[Verknüpfung von Aussagen]]logseq____",536870922]],[logseq____"^15logseq____",[207,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[207,logseq____"^Flogseq____",192,536870922]],[logseq____"^15logseq____",[207,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[207,logseq____"^Vlogseq____",202,536870922]],[logseq____"^15logseq____",[207,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[207,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[207,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[207,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",2],536870922]],[logseq____"^15logseq____",[207,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[207,logseq____"^Hlogseq____",184,536870922]],[logseq____"^15logseq____",[207,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[207,logseq____"^;logseq____",logseq____"~u652febdd-bc44-47e8-9bcd-311489103b62logseq____",536870922]],[logseq____"^15logseq____",[208,logseq____"^Qlogseq____",logseq____"Alternativ: $p\\\\equiv q$, falls $p\\\\leftrightarrow q$ [[Tantologie]]logseq____",536870922]],[logseq____"^15logseq____",[208,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[208,logseq____"^Flogseq____",211,536870922]],[logseq____"^15logseq____",[208,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[208,logseq____"^Vlogseq____",207,536870922]],[logseq____"^15logseq____",[208,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[208,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[208,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[208,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[208,logseq____"^Hlogseq____",174,536870922]],[logseq____"^15logseq____",[208,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[208,logseq____"^;logseq____",logseq____"~u652febdd-25b1-4d7a-ad2d-d0d0dd17a6dflogseq____",536870922]],[logseq____"^15logseq____",[209,logseq____"^Qlogseq____",logseq____"### [[Wahrheitswerteverlauf]] einer [[Aussageformel]]logseq____",536870922]],[logseq____"^15logseq____",[209,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[209,logseq____"^Flogseq____",196,536870922]],[logseq____"^15logseq____",[209,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[209,logseq____"^Vlogseq____",207,536870922]],[logseq____"^15logseq____",[209,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[209,logseq____"^Ulogseq____",168,536870922]],[logseq____"^15logseq____",[209,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[209,logseq____"^Ulogseq____",182,536870922]],[logseq____"^15logseq____",[209,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[209,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[209,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[209,logseq____"^Hlogseq____",168,536870922]],[logseq____"^15logseq____",[209,logseq____"^Hlogseq____",182,536870922]],[logseq____"^15logseq____",[209,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[209,logseq____"^;logseq____",logseq____"~u652febdd-8fca-4c65-baeb-8dc57d593737logseq____",536870922]],[logseq____"^15logseq____",[210,logseq____"^Qlogseq____",logseq____"[Variable]([[Variablen]]), die den Wert $w$ oder $f$ annimmtlogseq____",536870922]],[logseq____"^15logseq____",[210,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[210,logseq____"^Flogseq____",200,536870922]],[logseq____"^15logseq____",[210,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[210,logseq____"^Vlogseq____",200,536870922]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",169,536870922]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",176,536870922]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[210,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[210,logseq____"^Hlogseq____",176,536870922]],[logseq____"^15logseq____",[210,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[210,logseq____"^;logseq____",logseq____"~u652febdd-f6f0-475e-b987-73e50b7def3flogseq____",536870922]],[logseq____"^15logseq____",[211,logseq____"^Qlogseq____",logseq____"Formeln $p,q$ [logisch äquivalent]([[Logisch Äquivalent]]), wenn sie den gleichen [[Wahrheitswerteverlauf]] haben.\\n[[Schreibweise]]: $p\\\\equiv q$logseq____",536870922]],[logseq____"^15logseq____",[211,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[211,logseq____"^Flogseq____",195,536870922]],[logseq____"^15logseq____",[211,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[211,logseq____"^Vlogseq____",207,536870922]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",168,536870922]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",178,536870922]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[211,logseq____"^Ulogseq____",185,536870922]],[logseq____"^15logseq____",[211,logseq____"^Hlogseq____",168,536870922]],[logseq____"^15logseq____",[211,logseq____"^Hlogseq____",178,536870922]],[logseq____"^15logseq____",[211,logseq____"^Hlogseq____",185,536870922]],[logseq____"^15logseq____",[211,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[211,logseq____"^;logseq____",logseq____"~u652febdd-3f3b-4c66-8416-fabab4c283dblogseq____",536870922]],[logseq____"^15logseq____",[212,logseq____"^Qlogseq____",logseq____"### [[Tantologie]]logseq____",536870922]],[logseq____"^15logseq____",[212,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[212,logseq____"^Flogseq____",209,536870922]],[logseq____"^15logseq____",[212,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[212,logseq____"^Vlogseq____",207,536870922]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",174,536870922]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[212,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[212,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",3],536870922]],[logseq____"^15logseq____",[212,logseq____"^Jlogseq____",[],536870922]],[logseq____"^15logseq____",[212,logseq____"^Hlogseq____",174,536870922]],[logseq____"^15logseq____",[212,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[212,logseq____"^;logseq____",logseq____"~u652febdd-754e-4ede-bad5-6d1a5fa1e4e2logseq____",536870922]],[logseq____"^15logseq____",[213,logseq____"^Qlogseq____",logseq____"Satz, der wahr oder falsch ist, d.h. der [[Wahrheitswert]] $w$ bzw $f$ hat ($t/f$, $1/0$, $\\\\text{wahr}/\\\\text{falsch}$)logseq____",536870922]],[logseq____"^15logseq____",[213,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[213,logseq____"^Flogseq____",202,536870922]],[logseq____"^15logseq____",[213,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[213,logseq____"^Vlogseq____",202,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",172,536870922]],[logseq____"^15logseq____",[213,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[213,logseq____"^Hlogseq____",172,536870922]],[logseq____"^15logseq____",[213,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[213,logseq____"^;logseq____",logseq____"~u652febdd-292b-41a8-b152-d3ac7bce2ff5logseq____",536870922]],[logseq____"^15logseq____",[214,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n(p\\\\rightarrow q)logseq____&\\\\equiv((\\\\neg q)\\\\rightarrow(\\\\neg p))\\\\\\\\\\n(p\\\\land(p\\\\rightarrow q)) logseq____&\\\\rightarrow q logseq____&\\\\quad \\\\text{Tantologie}\\n\\\\end{align}logseq____",536870922]],[logseq____"^15logseq____",[214,logseq____"^Ologseq____",logseq____"^16logseq____",536870922]],[logseq____"^15logseq____",[214,logseq____"^Flogseq____",197,536870922]],[logseq____"^15logseq____",[214,logseq____"^Xlogseq____",165,536870922]],[logseq____"^15logseq____",[214,logseq____"^Vlogseq____",197,536870922]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",35,536870922]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",165,536870922]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",180,536870922]],[logseq____"^15logseq____",[214,logseq____"^Ulogseq____",184,536870922]],[logseq____"^15logseq____",[214,logseq____"^17logseq____",true,536870922]],[logseq____"^15logseq____",[214,logseq____"^;logseq____",logseq____"~u652febdd-c25d-4874-a757-ebf164af2556logseq____",536870922]],[logseq____"^15logseq____",[216,logseq____"^Klogseq____",1697639390088,536870923]],[logseq____"^15logseq____",[216,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[216,logseq____"^Ylogseq____",logseq____"regelnlogseq____",536870923]],[logseq____"^15logseq____",[216,logseq____"^11logseq____",logseq____"Regelnlogseq____",536870923]],[logseq____"^15logseq____",[216,logseq____"^Blogseq____",1697639390088,536870923]],[logseq____"^15logseq____",[216,logseq____"^;logseq____",logseq____"~u652febde-4e70-4727-9c73-e74d237399c4logseq____",536870923]],[logseq____"^15logseq____",[217,logseq____"^Klogseq____",1697639390078,536870923]],[logseq____"^15logseq____",[217,logseq____"^@logseq____",false,536870923]],[logseq____"^15logseq____",[217,logseq____"^Ylogseq____",logseq____"de morgansche regelnlogseq____",536870923]],[logseq____"^15logseq____",[217,logseq____"^11logseq____",logseq____"de Morgansche 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Bsp. $\\logseq____"17logseq____<y\\logseq____"$logseq____",536870923]],[logseq____"^15logseq____",[244,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[244,logseq____"^Flogseq____",253,536870923]],[logseq____"^15logseq____",[244,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[244,logseq____"^Vlogseq____",253,536870923]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[244,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[244,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[244,logseq____"^;logseq____",logseq____"~u652febde-ae55-4829-9f72-8eb6750c3bb2logseq____",536870923]],[logseq____"^15logseq____",[245,logseq____"^Qlogseq____",logseq____"see: [[Große Azzoziativgesetze]] [[Große de Morgansche Regeln]] [[Negationsregeln]]logseq____",536870923]],[logseq____"^15logseq____",[245,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[245,logseq____"^Flogseq____",250,536870923]],[logseq____"^15logseq____",[245,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[245,logseq____"^Vlogseq____",250,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",216,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",219,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",231,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[245,logseq____"^Ulogseq____",236,536870923]],[logseq____"^15logseq____",[245,logseq____"^Hlogseq____",219,536870923]],[logseq____"^15logseq____",[245,logseq____"^Hlogseq____",231,536870923]],[logseq____"^15logseq____",[245,logseq____"^Hlogseq____",236,536870923]],[logseq____"^15logseq____",[245,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[245,logseq____"^;logseq____",logseq____"~u652febde-dd8b-4009-8b85-7dd7b84aad8elogseq____",536870923]],[logseq____"^15logseq____",[246,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n(p\\\\land q)\\\\land r logseq____&\\\\equiv p\\\\land(q\\\\land r),\\\\quadlogseq____&\\\\text{schreibe daher: } p\\\\land q\\\\land r,\\\\quad \\\\land \\\\text{ assoziativ}\\\\\\\\\\n(p \\\\lor q) \\\\lor r logseq____&\\\\equiv p \\\\lor (q\\\\lor r),\\\\quadlogseq____&\\\\text{schreibe daher: } p\\\\lor q\\\\lor r,\\\\quad \\\\lor \\\\text{ assoziativ}\\\\\\\\\\np \\\\land q logseq____&\\\\equiv q \\\\land p,\\\\quad \\\\land logseq____&\\\\text{ kommutativ}\\\\\\\\\\np \\\\lor q logseq____&\\\\equiv q \\\\lor p,\\\\quad \\\\lor logseq____&\\\\text{ kommutativ}\\\\\\\\\\n\\\\neg(\\\\neg p) logseq____&\\\\equiv p, \\\\quad \\\\neg logseq____&\\\\text{ idenpotent}\\\\\\\\\\np\\\\land(q\\\\lor r)logseq____&\\\\equiv (p\\\\land q)\\\\lor(p\\\\land r);\\\\notag\\\\\\\\\\np\\\\lor(q\\\\land r)logseq____&\\\\equiv (p\\\\lor q)\\\\lor(p\\\\land r),\\\\quad logseq____&\\\\land,\\\\lor\\\\text{ wechselseitig distributiv}\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&\\\\equiv(\\\\neg p)\\\\lor(\\\\neg q);\\\\notag\\\\\\\\\\n\\\\neg(p\\\\land q)logseq____&\\\\equiv(\\\\neg p)\\\\land (\\\\neg q), \\\\quad logseq____&\\\\text{ (kleine) de Morgansche Regeln}\\\\\\\\\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[246,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[246,logseq____"^Flogseq____",263,536870923]],[logseq____"^15logseq____",[246,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[246,logseq____"^Vlogseq____",223,536870923]],[logseq____"^15logseq____",[246,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[246,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[246,logseq____"^;logseq____",logseq____"~u652febde-1348-418f-a181-af77d07ba496logseq____",536870923]],[logseq____"^15logseq____",[247,logseq____"^Qlogseq____",logseq____"wobei $\\\\pi$ eine \\logseq____"[[Permutation]]\\logseq____" der Zahl $(1,2,\\\\cdots,n)$ istlogseq____",536870923]],[logseq____"^15logseq____",[247,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[247,logseq____"^Flogseq____",256,536870923]],[logseq____"^15logseq____",[247,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[247,logseq____"^Vlogseq____",256,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",230,536870923]],[logseq____"^15logseq____",[247,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[247,logseq____"^Hlogseq____",230,536870923]],[logseq____"^15logseq____",[247,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[247,logseq____"^;logseq____",logseq____"~u652febde-1fe3-4a3a-a9b8-c966afedd045logseq____",536870923]],[logseq____"^15logseq____",[248,logseq____"^Qlogseq____",logseq____"Endliches Universum $U$ mit Objekten $O_1,\\\\cdots,O_m$logseq____",536870923]],[logseq____"^15logseq____",[248,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[248,logseq____"^Flogseq____",242,536870923]],[logseq____"^15logseq____",[248,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[248,logseq____"^Vlogseq____",252,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[248,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[248,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[248,logseq____"^;logseq____",logseq____"~u652febde-30ac-4f88-85ee-17e90b17b98blogseq____",536870923]],[logseq____"^15logseq____",[249,logseq____"^Qlogseq____",logseq____"Widerspruch = ↯, #logseq____",536870923]],[logseq____"^15logseq____",[249,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[249,logseq____"^Flogseq____",264,536870923]],[logseq____"^15logseq____",[249,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[249,logseq____"^Vlogseq____",264,536870923]],[logseq____"^15logseq____",[249,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[249,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[249,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[249,logseq____"^Ulogseq____",227,536870923]],[logseq____"^15logseq____",[249,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[249,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[249,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[249,logseq____"^;logseq____",logseq____"~u652febde-5806-4fc4-9038-a1fa7ee64226logseq____",536870923]],[logseq____"^15logseq____",[250,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\forall x:(p(x)\\\\land q(x)) logseq____&\\\\equiv (\\\\forall x: p(x)) \\\\land (\\\\forall x:q(x));\\\\notag\\\\\\\\\\n\\\\exists x: (p(x) \\\\lor q(x)) logseq____&\\\\equiv (\\\\exists x: p(x))\\\\lor(\\\\exists x: q(x)),\\\\quadlogseq____&\\\\text{Große Assoziativgesetze}\\\\\\\\\\n\\\\neg(\\\\forall x:p(x))logseq____&\\\\equiv \\\\exists x: (\\\\neg p(x));\\\\quadlogseq____&\\\\text{Große de Morgansche Regeln;}\\\\notag\\\\\\\\\\n\\\\neg(\\\\exists x: p(x)) logseq____&\\\\equiv \\\\forall x: (\\\\neg p(x)),\\\\quadlogseq____&\\\\text{Negationsregeln.}\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[250,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[250,logseq____"^Flogseq____",262,536870923]],[logseq____"^15logseq____",[250,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[250,logseq____"^Vlogseq____",262,536870923]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",216,536870923]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[250,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[250,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[250,logseq____"^;logseq____",logseq____"~u652febde-e1d2-481f-97ff-27f155d01696logseq____",536870923]],[logseq____"^15logseq____",[251,logseq____"^Qlogseq____",logseq____"Sei $x$ aus $\\\\Reals$ beliebig. Setze $y:=x+1$ (ist aus $\\\\Reals$). Dann ist $xlogseq____<x+1=y$ also $xlogseq____<y$. $\\\\blacksquare$logseq____",536870923]],[logseq____"^15logseq____",[251,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[251,logseq____"^Flogseq____",255,536870923]],[logseq____"^15logseq____",[251,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[251,logseq____"^Vlogseq____",255,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",227,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[251,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[251,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[251,logseq____"^;logseq____",logseq____"~u652febde-5493-481f-b397-08555a089e53logseq____",536870923]],[logseq____"^15logseq____",[252,logseq____"^Qlogseq____",logseq____"# [[Aussageform]]logseq____",536870923]],[logseq____"^15logseq____",[252,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[252,logseq____"^Flogseq____",246,536870923]],[logseq____"^15logseq____",[252,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[252,logseq____"^Vlogseq____",223,536870923]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[252,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[252,logseq____"^?logseq____",[logseq____"^ logseq____",logseq____"^18logseq____",1],536870923]],[logseq____"^15logseq____",[252,logseq____"^Jlogseq____",[],536870923]],[logseq____"^15logseq____",[252,logseq____"^Hlogseq____",234,536870923]],[logseq____"^15logseq____",[252,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[252,logseq____"^;logseq____",logseq____"~u652febde-3c27-43cd-9878-20446c9d096blogseq____",536870923]],[logseq____"^15logseq____",[253,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\logseq____"\\\\text{x ist prim}\\logseq____" \\\\quad logseq____& \\\\text{ist AF mit Variablen x über den natürlichen Zahlen}\\\\\\\\\\n\\logseq____"\\\\underbrace{x}_{x_1}logseq____<\\\\underbrace{y}_{x_2}\\logseq____"\\\\quad logseq____&\\\\text{ist AF mit Variablen }x,y\\\\text{ über die reellen Zahlen } \\\\underbrace{\\\\Reals}_{U_1},\\\\underbrace{\\\\Reals}_{U_2}\\\\\\\\\\n\\logseq____"\\\\text{x ist wahr}\\logseq____"\\\\quadlogseq____&\\\\text{ist AF mit Variablen x über dem Universum der Aussagen}\\n\\\\end{align}logseq____",536870923]],[logseq____"^15logseq____",[253,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[253,logseq____"^Flogseq____",261,536870923]],[logseq____"^15logseq____",[253,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[253,logseq____"^Vlogseq____",252,536870923]],[logseq____"^15logseq____",[253,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[253,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[253,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[253,logseq____"^;logseq____",logseq____"~u652febde-9da2-4783-aa04-20584a227dbblogseq____",536870923]],[logseq____"^15logseq____",[254,logseq____"^Qlogseq____",logseq____"Betrachte $\\logseq____"xlogseq____<y\\logseq____"$ als AF über $\\\\Reals, \\\\Reals$logseq____",536870923]],[logseq____"^15logseq____",[254,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[254,logseq____"^Flogseq____",277,536870923]],[logseq____"^15logseq____",[254,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[254,logseq____"^Vlogseq____",277,536870923]],[logseq____"^15logseq____",[254,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[254,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[254,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[254,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[254,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[254,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[254,logseq____"^;logseq____",logseq____"~u652febde-80e0-4201-94f3-cce8d28b1142logseq____",536870923]],[logseq____"^15logseq____",[255,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____<y\\\\quad\\\\text{ist wahr}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____",536870923]],[logseq____"^15logseq____",[255,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[255,logseq____"^Flogseq____",254,536870923]],[logseq____"^15logseq____",[255,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[255,logseq____"^Vlogseq____",254,536870923]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",227,536870923]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[255,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[255,logseq____"^Hlogseq____",227,536870923]],[logseq____"^15logseq____",[255,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[255,logseq____"^;logseq____",logseq____"~u652febde-11e1-4901-af54-aa1cbba11803logseq____",536870923]],[logseq____"^15logseq____",[256,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\nlogseq____&\\\\forall x: \\\\forall y: p(x, y) \\\\equiv \\\\forall y: \\\\forall x: p(x,y)\\\\\\\\\\nlogseq____&\\\\exists x:\\\\exists y:p(x,y)\\\\equiv\\\\exists y:\\\\exists x:p(x,y)\\\\\\\\\\nlogseq____&[\\\\forall x_1:\\\\forall x_2: \\\\cdots:\\\\forall x_n:p(x_1,x_2,\\\\cdots,x_n)\\\\notag\\\\\\\\\\nlogseq____&\\\\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____",536870923]],[logseq____"^15logseq____",[256,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[256,logseq____"^Flogseq____",243,536870923]],[logseq____"^15logseq____",[256,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[256,logseq____"^Vlogseq____",243,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[256,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[256,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[256,logseq____"^;logseq____",logseq____"~u652febde-f1a3-47df-87c4-5f22f23aa638logseq____",536870923]],[logseq____"^15logseq____",[257,logseq____"^Qlogseq____",logseq____"Die beiden Quantoren $\\\\forall, \\\\exists$ erweitern die [Sprache]([[Sprachen]]) der [[Aussagenlogik]]logseq____",536870923]],[logseq____"^15logseq____",[257,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[257,logseq____"^Flogseq____",269,536870923]],[logseq____"^15logseq____",[257,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[257,logseq____"^Vlogseq____",252,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",220,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[257,logseq____"^Ulogseq____",239,536870923]],[logseq____"^15logseq____",[257,logseq____"^Hlogseq____",220,536870923]],[logseq____"^15logseq____",[257,logseq____"^Hlogseq____",239,536870923]],[logseq____"^15logseq____",[257,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[257,logseq____"^;logseq____",logseq____"~u652febde-f5fa-48d5-b787-26351297e2f9logseq____",536870923]],[logseq____"^15logseq____",[258,logseq____"^Qlogseq____",logseq____"$\\\\exists x:p(x)$ ist die Aussage: \\logseq____"Es gibt (wenigstens) ein x aus U für das $p(x)$ wahr ist\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w \\\\quadlogseq____&\\\\text{falls }p(x)\\\\text{ w ist für (wenigstens) ein x aus U}\\\\\\\\f\\\\quad logseq____&\\\\text{falls }p(x)\\\\text{ f ist für alle x aus U}\\\\end{cases}$logseq____",536870923]],[logseq____"^15logseq____",[258,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[258,logseq____"^Flogseq____",275,536870923]],[logseq____"^15logseq____",[258,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[258,logseq____"^Vlogseq____",252,536870923]],[logseq____"^15logseq____",[258,logseq____"^Ulogseq____",172,536870923]],[logseq____"^15logseq____",[258,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[258,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[258,logseq____"^Hlogseq____",172,536870923]],[logseq____"^15logseq____",[258,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[258,logseq____"^;logseq____",logseq____"~u652febde-6b69-4f79-acce-6d87f0938f6blogseq____",536870923]],[logseq____"^15logseq____",[259,logseq____"^Qlogseq____",logseq____"$\\\\forall x:p(x)$ ist die [Aussage]([[Aussagen]]): $\\logseq____"\\\\text{Für alle x aus U ist p(x) wahr}\\logseq____"\\nIhr [[Wahrheitswert]] ist $\\\\begin{cases}w\\\\quadlogseq____&\\\\text{fallls p(x) w für alle x aus U}\\\\\\\\f\\\\quadlogseq____&\\\\text{falls p(x) f für (wenigstens) ein x aus U}\\\\end{cases}$logseq____",536870923]],[logseq____"^15logseq____",[259,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[259,logseq____"^Flogseq____",269,536870923]],[logseq____"^15logseq____",[259,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[259,logseq____"^Vlogseq____",269,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",172,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",180,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[259,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[259,logseq____"^Hlogseq____",172,536870923]],[logseq____"^15logseq____",[259,logseq____"^Hlogseq____",180,536870923]],[logseq____"^15logseq____",[259,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[259,logseq____"^;logseq____",logseq____"~u652febde-a5ea-417a-8a97-f6fed6bf3563logseq____",536870923]],[logseq____"^15logseq____",[260,logseq____"^Qlogseq____",logseq____"[[Aussageform]] (AF) über [Universen]([[Universen (Logik)]]) $U_1,\\\\cdots,U_n$:logseq____",536870923]],[logseq____"^15logseq____",[260,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[260,logseq____"^Flogseq____",252,536870923]],[logseq____"^15logseq____",[260,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[260,logseq____"^Vlogseq____",252,536870923]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[260,logseq____"^Ulogseq____",238,536870923]],[logseq____"^15logseq____",[260,logseq____"^Hlogseq____",234,536870923]],[logseq____"^15logseq____",[260,logseq____"^Hlogseq____",238,536870923]],[logseq____"^15logseq____",[260,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[260,logseq____"^;logseq____",logseq____"~u652febde-243a-4166-b724-0dbcfee4f961logseq____",536870923]],[logseq____"^15logseq____",[261,logseq____"^Qlogseq____",logseq____"[[Beispiele]]logseq____",536870923]],[logseq____"^15logseq____",[261,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[261,logseq____"^Flogseq____",265,536870923]],[logseq____"^15logseq____",[261,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[261,logseq____"^Vlogseq____",252,536870923]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[261,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[261,logseq____"^Hlogseq____",35,536870923]],[logseq____"^15logseq____",[261,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[261,logseq____"^;logseq____",logseq____"~u652febde-6c3a-405c-9fef-a7e0662bf512logseq____",536870923]],[logseq____"^15logseq____",[262,logseq____"^Qlogseq____",logseq____"## [[Regeln]]logseq____",536870923]],[logseq____"^15logseq____",[262,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[262,logseq____"^Flogseq____",274,536870923]],[logseq____"^15logseq____",[262,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[262,logseq____"^Vlogseq____",252,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",216,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[262,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[262,logseq____"^?logseq____",[logseq____"^ 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[[Regeln]]logseq____",536870923]],[logseq____"^15logseq____",[263,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[263,logseq____"^Flogseq____",223,536870923]],[logseq____"^15logseq____",[263,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[263,logseq____"^Vlogseq____",223,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",216,536870923]],[logseq____"^15logseq____",[263,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[263,logseq____"^?logseq____",[logseq____"^ 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$\\\\blacksquare$logseq____",536870923]],[logseq____"^15logseq____",[264,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[264,logseq____"^Flogseq____",270,536870923]],[logseq____"^15logseq____",[264,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[264,logseq____"^Vlogseq____",270,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",227,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[264,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[264,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[264,logseq____"^;logseq____",logseq____"~u652febde-ded6-4241-81da-b2bbf8e34b7elogseq____",536870923]],[logseq____"^15logseq____",[265,logseq____"^Qlogseq____",logseq____"[[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____",536870923]],[logseq____"^15logseq____",[265,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[265,logseq____"^Flogseq____",260,536870923]],[logseq____"^15logseq____",[265,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[265,logseq____"^Vlogseq____",252,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",176,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",180,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",237,536870923]],[logseq____"^15logseq____",[265,logseq____"^Ulogseq____",240,536870923]],[logseq____"^15logseq____",[265,logseq____"^Hlogseq____",176,536870923]],[logseq____"^15logseq____",[265,logseq____"^Hlogseq____",180,536870923]],[logseq____"^15logseq____",[265,logseq____"^Hlogseq____",237,536870923]],[logseq____"^15logseq____",[265,logseq____"^Hlogseq____",240,536870923]],[logseq____"^15logseq____",[265,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[265,logseq____"^;logseq____",logseq____"~u652febde-0940-4db1-aa8c-09a6e9af89aalogseq____",536870923]],[logseq____"^15logseq____",[266,logseq____"^Qlogseq____",logseq____"[Beispiel]([[Beispiele]])logseq____",536870923]],[logseq____"^15logseq____",[266,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[266,logseq____"^Flogseq____",243,536870923]],[logseq____"^15logseq____",[266,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[266,logseq____"^Vlogseq____",252,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[266,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[266,logseq____"^Hlogseq____",35,536870923]],[logseq____"^15logseq____",[266,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[266,logseq____"^;logseq____",logseq____"~u652febde-b2dd-4709-b084-68dbcd10ef8flogseq____",536870923]],[logseq____"^15logseq____",[267,logseq____"^Qlogseq____",logseq____"$\\\\blacksquare$ = Beweisende, auch [q.e.d.]([[Q.E.D.]]), [[w.z.b.w.]], QED, 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x :\\\\exists y :\\\\forall w :\\\\forall u :\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)\\\\right)\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x:(\\\\neg(\\\\exists y: \\\\forall w: \\\\forall u: \\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x:\\\\forall y:(\\\\neg(\\\\forall w: \\\\forall u:\\\\exists z: p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x:\\\\forall y:\\\\exists w:(\\\\neg(\\\\forall u:\\\\exists z:p(x,y,z)\\\\rightarrow q(u,w)))\\\\\\\\\\n\\\\equivlogseq____&\\\\exists x: \\\\forall y: \\\\exists w: \\\\exists u : \\\\forall z:\\\\neg(p(x,y,z)\\\\rightarrow 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$U$:logseq____",536870923]],[logseq____"^15logseq____",[269,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[269,logseq____"^Flogseq____",253,536870923]],[logseq____"^15logseq____",[269,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[269,logseq____"^Vlogseq____",252,536870923]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[269,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[269,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[269,logseq____"^;logseq____",logseq____"~u652febde-fda6-4d7c-8bd1-3c6a672c7565logseq____",536870923]],[logseq____"^15logseq____",[270,logseq____"^Qlogseq____",logseq____"\\\\begin{align}\\n\\\\forall x:\\\\exists y:xlogseq____<y\\\\quad\\\\text{ist falsch}\\n\\\\end{align}\\n[Beweis]([[Beweise]]):logseq____",536870923]],[logseq____"^15logseq____",[270,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[270,logseq____"^Flogseq____",255,536870923]],[logseq____"^15logseq____",[270,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[270,logseq____"^Vlogseq____",254,536870923]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",35,536870923]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",224,536870923]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",227,536870923]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",228,536870923]],[logseq____"^15logseq____",[270,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[270,logseq____"^Hlogseq____",227,536870923]],[logseq____"^15logseq____",[270,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[270,logseq____"^;logseq____",logseq____"~u652febde-73e2-4a74-84f1-c2d8d9df510blogseq____",536870923]],[logseq____"^15logseq____",[271,logseq____"^Qlogseq____",logseq____"#FIXMElogseq____",536870923]],[logseq____"^15logseq____",[271,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[271,logseq____"^Flogseq____",274,536870923]],[logseq____"^15logseq____",[271,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[271,logseq____"^Vlogseq____",274,536870923]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",42,536870923]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[271,logseq____"^Ulogseq____",234,536870923]],[logseq____"^15logseq____",[271,logseq____"^Hlogseq____",42,536870923]],[logseq____"^15logseq____",[271,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[271,logseq____"^;logseq____",logseq____"~u652febde-d85f-425c-9fc2-6ed46ed89502logseq____",536870923]],[logseq____"^15logseq____",[272,logseq____"^Qlogseq____",logseq____"see: [[assoziativ]] [[kommutativ]] [[idenpotent]] [[wechselseitig distributiv]] [[distributiv]] [[de Morgansche Regeln]]logseq____",536870923]],[logseq____"^15logseq____",[272,logseq____"^Ologseq____",logseq____"^16logseq____",536870923]],[logseq____"^15logseq____",[272,logseq____"^Flogseq____",246,536870923]],[logseq____"^15logseq____",[272,logseq____"^Xlogseq____",223,536870923]],[logseq____"^15logseq____",[272,logseq____"^Vlogseq____",246,536870923]],[logseq____"^15logseq____",[272,logseq____"^Ulogseq____",217,536870923]],[logseq____"^15logseq____",[272,logseq____"^Ulogseq____",222,536870923]],[logseq____"^15logseq____",[272,logseq____"^Ulogseq____",223,536870923]],[logseq____"^15logseq____",[272,logseq____"^Ulogseq____",225,536870923]],[logseq____"^15logseq____",[272,logseq____"^Ulogseq____",226,536870923]],[logseq____"^15logseq____",[272,logseq____"^Ulogseq____",232,536870923]],[logseq____"^15logseq____",[272,logseq____"^Ulogseq____",233,536870923]],[logseq____"^15logseq____",[272,logseq____"^Hlogseq____",217,536870923]],[logseq____"^15logseq____",[272,logseq____"^Hlogseq____",222,536870923]],[logseq____"^15logseq____",[272,logseq____"^Hlogseq____",225,536870923]],[logseq____"^15logseq____",[272,logseq____"^Hlogseq____",226,536870923]],[logseq____"^15logseq____",[272,logseq____"^Hlogseq____",232,536870923]],[logseq____"^15logseq____",[272,logseq____"^Hlogseq____",233,536870923]],[logseq____"^15logseq____",[272,logseq____"^17logseq____",true,536870923]],[logseq____"^15logseq____",[272,logseq____"^;logseq____",logseq____"~u652febde-1c4e-41dc-a92c-b8bee9e78d4blogseq____",536870923]],[logseq____"^15logseq____",[273,logseq____"^Qlogseq____",logseq____"Schachtelung von quantoren 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