Q40 of 58 Page 12

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

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

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