If A and B are two sets, then A ∩ (A ∪ B) equals

Question

Philoid · Accepted Answer

Given: A and B are two given sets

To find: A ∩ (A ∪ B)

Let x ∈ A ∩ (A ∪ B)

⇒ x ∈ A and x ∈ (A ∪ B)

⇒ x ∈ A and (x ∈ A or x ∈ B)

⇒ (x ∈ A and x ∈ A) or (x ∈ A and x ∈ B)

⇒ x ∈ A or x ∈ A ∩ B

⇒ x ∈ A

Hence, A ∩ (A ∪ B) = A