logical_equivalences

Logical Equivalences Name Equivalence Identity laws p ∧ T ≡ p p ∨ F ≡ p Domination laws p ∨ T ≡ T p ∧ F ≡ F Idempotent laws p ∨ p ≡ p p ∧ p ≡ p Double negation law ∼ ( ∼ p ) ≡ p Commutative laws p ∨ q ≡ q ∨ p p ∧ q ≡ q ∧ p Associative laws ( p ∨ q ) ∨ r ≡ p ∨ ( q ∨ r ) ( p ∧ q ) ∧ r ≡ p ∧ ( q ∧ r ) Distributive laws p ∨ ( q ∧ r ) ≡ ( p ∨ q ) ∧ ( p ∨ r ) p ∧ ( q ∨ r ) ≡ ( p ∧ q ) ∨ ( p ∧ r ) DeMorgan’s laws ∼ ( p ∧ q ) ≡∼ p ∨ ∼ q ∼ ( p ∨ q ) ≡∼ p ∧ ∼ q Absorption laws p ∨ ( p ∧ q ) ≡ p p ∧ ( p ∨ q ) ≡ p Negation laws p ∨ ∼ p ≡ T p ∧ ∼ p ≡ F Credit : Discrete Math and its Applications (7th), Kenneth Rosen, pg. 27 1