Axioms in set theory

Idempotence A = A ∪ A A = A ∩ A

Domination A ∪ U = U A ∩ ∅ = ∅

Identity A ∪ ∅ = A A ∩ U = A

Double complement A = A''

DeMorgan's laws (A ∪ B)' = A' ∩ B' (A ∩ B)' = A' ∪ B'

Commutative laws A ∪ B = B ∪ A A ∩ B = B ∩ A

Associative laws (A ∪ B) ∪ C = A ∪ (B ∪ C) (A ∩ B) ∩ C = A ∩ (B ∩ C)

Distributive laws A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

Absorption laws A ∪ (A ∩ B) = A A ∩ (A ∪ B) = A