Logic law (tautology) is always true, independently from values of variables p, q, r, ... which it is compound. Commutative law for conjunction: p ∧ q ⇔ q ∧ p. Commutative law for disjunction: p ∨ q ⇔ q ∨ p. Associative law for conjunction: (p ∧ q) ∧ r ⇔ p ∧ (q ∧ r). Associative law for disjunction: (p ∨ q) ∨ r ⇔ p ∨ (q ∨ r). Distributive law for conjunction over disjunction: p ∧ (q ∨ r) ⇔ (p ∧ q) ∨ (p ∧ r). Distributive law for disjunction over conjunction: p ∨ (q ∧ r) ⇔ (p ∨ q) ∧ (p ∨ r). Involution law: ~(~p) ⇔ p. Negation conditional law: ~(p ⇒ q) ⇔ (p ∧ ~q). De Morgan's laws: ~(p ∧ q) ⇔ (~p) ∨ (~q), ~(p ∨ q) ⇔ (~p) ∧ (~q). De Morgan's laws for statement with quantifiers: ~(∀x p(x)) ⇔ ∃x (~p(x)), ~(∃x q(x)) ⇔ ∀x (~q(x)).