Question

For any two sets, prove that:
(i) A ∪ (A ∩ B) = A

(ii) A ∩ (A ∪ B) = A

Answer 1

(i) A ∪ (A ∩ B) = A

As we know union is distributive over intersection

Therefore, A ∪ (A ∩ B)

(A ∪ A) ∩ (A ∪ B) [Here, A ∪ A = A]

A ∩ (A ∪ B)

A

(ii) A ∩ (A ∪ B) = A

As we know union is distributive over intersection

Therefore, (A ∩ A) ∪ (A ∩ B)

A ∪ (A ∩ B) [Here, A ∩ A = A]

A