Question

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

Answer 1

(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 {from (1)}