Math 125 Set Identities

Commutative Laws

For all sets A and B, A U B = B U A and A n B = B n A

Associative Laws

For all sets A, B, and C, (A U B) U C = A U (B U C), and (A n B) n c = A n (B n C)

Distributive Laws

For all sets A, B and C, A U (B n C) = (A U B) n (A U C) and A n (B U C ) = (A n B) U (A n C)

Identity Laws

For every set A, A U 0 = A and A n U = A

Compliment Laws

For every set A, A U A^c = U and A n A^c = 0

Double Compliment Law

For every set A, (A^c)^c = A

Idempotent Laws

For every set A, A U A = A and A n A = A

Universal Bound Laws

For every set A, A u U = U and A n 0 = 0

De Morgan's Laws

For all sets A and B, (A U B)^c = A^c n B^c and (A n B)^c = A^c U B^c

Absorption Laws

For all sets A and B, A U (A n B) = A and A n (A U B) = A

Compliments of U and 0

U^c = 0 and 0^c = U

Set Difference Law

For all sets A and B, A - B = A n B^c