Using properties of sets, show that (i) A∪(A∩B)=A (ii) A∩(A∪B)=A

(i) To show: A∪(A∩B)=A
We know that A⊆A ⇒ A∩B⊆A ⇒ A∪(A∩B)⊆A. (1)
Also, A⊆A∪(A∩B) (2)
From (1) and (2), A∪(A∩B)=A
(ii) To show: A∩(A∪B)=A
A∩(A∪B)=(A∩A)∪(A∩B)=A∪(A∩B)=A (by (i))
⇒A∩(A∪B)=A