Set identities

there's no math tag? really?

Commutative law

A ∪ B = B ∪ A

A ∩ B = B ∩ A

Associative law

(A ∪ B) ∪ C = A ∪ (B ∪ C)

(A ∩ B) ∩ C = A ∩ (B ∩ C)

Distributive law

A ∩ (B ∪ C) = (A ∪ B) ∩ (A ∪ C)

A ∪ (B ∩ C) = (A ∩ B) ∪ (A ∩ C)

Identity laws

A ∪ ∅ = A

A ∩ U = A

Complement laws

A ∪ A^c = U

A ∩ A^c = ∅

Double complement law

((A)^c)^c = A

Idempotent laws

A ∩ A = A

A ∪ A = A

Universal bound laws

A ∪ U = U

A ∩ ∅ = ∅

De Morgan’s Laws

(A ∪ B)^c = A^c ∩ B^c

(A ∩ B)^c = A^c ∪ B^c

Absorption laws

A ∪ (A ∩ B) = A

A ∩ (A ∪ B) = A

Set Difference law

A - B = A ∩ B^c