# Algèbre de Boole

 Théorème Forme AND Forme OR Théorème Forme AND Forme OR Involution ¬¬p = p Idempotence p . p = p p + p = p Identité p . 1 = pp . 0 = 0 p + 1 = 1p + 0 = p Complémentarité p . ¬p= 0 p + ¬p= 1 Commutativité p . q = q . p p + q = q + p Associativité (p . q) . r = p . (q . r) (p + q) + r = p + (q + r) Distributivité p + q . r = (p + q) . (p + r) p . (q + r) = p . q + p . r Lois de de Morgan ¬(p + q) = ¬p . ¬q ¬(p . q) = ¬p + ¬q Implication p ==> q = ¬p + q Contraposition p ==> q = ¬q ==>¬p Absorption p . (p + q) = pp . (¬p + q) = p . q p + (p . q) = pp + (¬p . q) = p + q Rappels Définition du OU exclusif : p ⊕ q = ¬p . q + p . ¬qDéfinition de l'équivalence : p°q = p . q + ¬p . ¬q

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