For any sets A and B, prove that: (i) A∪(A∩B)=A
(ii) A∩(A∪B)=A
(i) Since (A∩B)⊆A, we have A∪(A∩B)=A[∵X⊆Y⇒X∪Y=Y]
(ii) Since A⊆(A∪B), we have A∩(A∪B)=A[∵X⊆Y⇒X∩Y=X]
(Idempotent laws) For any set A, prove that: (i) A∪A=A
(ii) A∩A=A
(De Morgan's laws) For any two sets A and B, prove that: I. (A∪B)′=(A′∩B′)
II. (A∩B)′=(A′∪B′)
(Commultative laws) For any two sets a and B, prove that: I. A∪B=B∪A [Commutative law for union of sets]
II. A∩B=B∩A [Commutative law for intersection of sets]