Logique - Synthèse

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Synthèses sur quelques notions de logique

Last updated 1:42 PM on 6/29/23
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23 Terms

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¬
négation(non)
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disjonction (ou)
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conjonction(et)
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implication (si...alors...)
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équivalence (...si et seulement si ...)
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Tautologie
Une formule toujours vraie
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L'équivalence entre formules
Ф1 ⇔ Ф2 \=\> une tautologie
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pour tout
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il existe
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La contraposée de P⇒Q
¬Q ⇒ ¬P
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La réciproque de P⇒Q
Q ⇒ P
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Prouver que la formule Ф est fausse
Prouver que ¬Q est vrai
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Preuve par induction de P(x)
Case de base P(0)

Cas général: P(n) = P(n+1)
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Un ensemble
Une connection d'objet appelés éléments
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Un ensemble en extension
Les éléments distingués explicitement. Ex: {a,b}
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Un ensemble en compréhension
formules qui décrit exactement les éléments de l'ensemble. Ex: {x | P(x)}
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f: A → B, f est injective
∀ a1,a2 € A; f(a1)\=f(a2) ⇒ a1\=a2
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f: A → B, f est surjective
∀ b € B, ∃ a € A f(a)\= b
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Surjective
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Injective
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¬(P⇒Q)
P ∧ ¬Q
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√(x)\=y
(y²\= x ∧ y ≥ 0 )
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F est croissante
∀a,b ∈ Dom f, a≤b →f(a)≤f(b)

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