If A and B are two sets,

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

(a) A

(b) B

(c) ϕ

(d) A ∩ B

Solution:

A ∩ (A ⋃ B)

= (A ∩ A) ⋃ (A ∩ B)

= A ⋃ (A ∩ B)

A ∩ (A ⋃ B) = A

(since A ∩ B ≤ A)

Hence, the correct answer is option A.