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NDA 2026 · PYQ · Set Theory · medium

What is (((A ∩ B) ∪ (A - B)) - ((A ∩ B) ∪ (B - A))) ∪ A equal to?

Answer

The correct answer is B: A. (A ∩ B) ∪ (A - B) = A and (A ∩ B) ∪ (B - A) = B. So expression becomes (A - B) ∪ A = A (since A - B ⊆ A).

  1. A.φ
  2. B.A✓ Correct
  3. C.B
  4. D.A ∪ B

Explanation

(A ∩ B) ∪ (A - B) = A and (A ∩ B) ∪ (B - A) = B. So expression becomes (A - B) ∪ A = A (since A - B ⊆ A). Therefore the answer is A.
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