- Identität
![{\displaystyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3) |
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![{\displaystyle 1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf) |
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- Negation
![{\displaystyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3) |
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![{\displaystyle 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950) |
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- Tautologie
![{\displaystyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3) |
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![{\displaystyle 1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf) |
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- Kontradiktion; Widerspruch
![{\displaystyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3) |
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![{\displaystyle 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950) |
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- Äquivalenz
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![{\displaystyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3) |
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![{\displaystyle B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a) |
![{\displaystyle 1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf) |
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![{\displaystyle \neg B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a8cf55d88686624cd054232a7cf1a6b7e6e84210) |
![{\displaystyle 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950) |
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- Implikation
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![{\displaystyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3) |
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![{\displaystyle B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a) |
![{\displaystyle 1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf) |
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![{\displaystyle \neg B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a8cf55d88686624cd054232a7cf1a6b7e6e84210) |
![{\displaystyle 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950) |
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- Disjunktion
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![{\displaystyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3) |
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![{\displaystyle B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a) |
![{\displaystyle 1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf) |
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![{\displaystyle \neg B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a8cf55d88686624cd054232a7cf1a6b7e6e84210) |
![{\displaystyle 1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf) |
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- Konjunktion
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![{\displaystyle A}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3) |
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![{\displaystyle B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a) |
![{\displaystyle 1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/92d98b82a3778f043108d4e20960a9193df57cbf) |
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![{\displaystyle \neg B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a8cf55d88686624cd054232a7cf1a6b7e6e84210) |
![{\displaystyle 0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950) |
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Kommutativgesetz
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![{\displaystyle A\lor B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9b9c9c90857c12727201dd9e47a4e7c8658fdbc5) |
![{\displaystyle \Leftrightarrow }](https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf) |
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![{\displaystyle A\land B}](https://wikimedia.org/api/rest_v1/media/math/render/svg/74954195333a8593163b93a9688695b8dc74da55) |
![{\displaystyle \Leftrightarrow }](https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf) |
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Assoziativität
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![{\displaystyle A\lor \left(B\lor C\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/adae884bbcce37cfa95e7a972f63cde150cf6f3e) |
![{\displaystyle \Leftrightarrow }](https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf) |
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![{\displaystyle A\land \left(B\land C\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ded94060450628c7ed4612fcf59e7e2f8bdb46c) |
![{\displaystyle \Leftrightarrow }](https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf) |
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Distributivität
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Implikation
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Verschmelzungsgesetz
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Dualität
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Doppelnegation
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Tautologie
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Widerspruch
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- Symbole
Logiksymbole
![{\displaystyle \neg }](https://wikimedia.org/api/rest_v1/media/math/render/svg/fa78fd02085d39aa58c9e47a6d4033ce41e02fad) |
![{\displaystyle \Rightarrow }](https://wikimedia.org/api/rest_v1/media/math/render/svg/469b737d167b9b28a74e27c7f5e35b5ea9256100) |
![{\displaystyle \exists }](https://wikimedia.org/api/rest_v1/media/math/render/svg/77ed842b6b90b2fdd825320cf8e5265fa937b583) |
![{\displaystyle \forall }](https://wikimedia.org/api/rest_v1/media/math/render/svg/bfc1a1a9c4c0f8d5df989c98aa2773ed657c5937) |
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![{\displaystyle \lor }](https://wikimedia.org/api/rest_v1/media/math/render/svg/ab47f6b1f589aedcf14638df1d63049d233d851a) |
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Nicht |
Folgt |
Existiert Existenzquantor |
für alle Allquantor |
gleich |
oder |
und
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- Logik
- Variablen
- Konstanten
- Prädikate
- Funktionen
- Funktionssymbole sind spezifisch in der beschriebenen Sprache (etwa Natürliche Zahlen)
- Terme
Term
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variabler Term |
konstanter Term
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Variabel |
Konstante
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Funktion(Term,Term,Term) |
keine Variablen
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Primformel |
Bedingung
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Gleichungen aus Termen
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- R ist Prädikat
- t1…tn sind Term
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Formel |
Bedingung
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![{\displaystyle F}](https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57) |
Primformel
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F,G : Formel
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- wenn vor der Variablen x kein Quantor steht ist sie frei
![{\displaystyle (\forall x)((\forall y)F)\Leftrightarrow (\forall x)(\forall y)F}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f3a11447134b6956acebf2b6356ee4033a31d1ef)
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- Wichtige Funktionswerte
Winkel
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Sinus
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Kosinus
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Tangens
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nicht definiert
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nicht definiert
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- Sinussatz
![{\displaystyle {\frac {a}{\sin \alpha }}={\frac {b}{\sin \beta }}={\frac {c}{\sin \gamma }}=2\,r={\frac {u}{\pi }}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ae3a55c93d9e1cf7bc9fff94d95ca6243426669e)
- Kosinussatz
![{\displaystyle c^{2}=a^{2}+b^{2}-2\,a\,b\,\cos \gamma \qquad \left\|{\vec {c}}\right\|^{2}=\left\|{\vec {a}}\right\|^{2}+\left\|{\vec {b}}\right\|^{2}-2\,{\vec {a}}\,{\vec {b}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9ae89d4a455b8ef67eeeacdedd536fcedb91281b)
- Hyperbelfunktionen
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- Kofunktionen
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siehe auch: Vorlage:Umrechnungstabelle Trigonometrie
- Moivrescher Satz
![{\displaystyle \left(\cos x+i\,\sin x\right)^{n}=\cos \left(n\,x\right)+i\,\sin \left(n\,x\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bcfd68baead6527d4ebb70e9d8f4865fca28123e)
![{\displaystyle \cos x+i\,\sin x=\operatorname {cis} \,x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a239396b030ff073b1fe7be62ff83376292ed3d1)
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