Discrete Math

Commutative laws

p ∧ q ≡ q ∧ p and p ∨ q ≡ q ∨ p

Associative laws

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r) and (p ∨ q) ∨ r ≡ p ∨ (q ∨ r)

Distributive laws

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r) and p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)

Identity laws

p ∧ t ≡ p and p ∨ c ≡ p

Negation laws

p ∨ ~p ≡ t and p ∧ ~p ≡ c

Double negative law

~(~p) ≡ p

Idempotent laws

p ∧ p ≡ p and p ∨ p ≡ p

Universal bound laws

p ∨ t ≡ t and p ∧ c ≡ c

De Morgan's laws

~(p ∧ q) ≡ ~p ∨ ~q and ~(p ∨ q) ≡ ~p ∧ ~q

Absorption laws

p ∨ (p ∧ q) ≡ p and p ∧ (p ∨ q) ≡ p

Negations of t and c

~t ≡ c and ~c ≡ t