Laws of algebra of sets

1. Idempotent laws

(i) A U A = A
(ii) A ∩ A = A

2. Identity laws

(i) A U ф = A
(ii) A ∩ U = A

3. Commutative law
(i) A U B = B U A
(ii) A ∩ B = B ∩ A

4. Associative laws

(i) (A U B) U C = A U (B U C)
(ii) (A ∩ B) ∩ C = A ∩ (B ∩ C)

5. Distributive laws

(i) A U (B ∩ C) = (A U B) ∩ (A U C)
(ii) A ∩ (B U C) = (A ∩ B) U (A ∩ C)

6. De-morgan’s laws

(i) (A U B)’ = A’ ∩ B’
(ii) (A ∩ B)’ = A’ U B’