Let A and B be sets and let A' and B' denote the complements of the sets A and B. The set (A - B) ∪ (B - A) ∪ (A ∩ B) is equal to: A. A ∪ B B. A' ∪ B' C. A ∩ B D. A' ∩ B'

GATE 1996 · Discrete Mathematics · Set Theory · easy

Answer: A. A ∪ B

1. Express each part using intersections and complements: (A - B) ∪ (B - A) ∪ (A ∩ B) = (A ∩ B') ∪ (B ∩ A') ∪ (A ∩ B)
2. Show the union equals A ∪ B: (A ∩ B') ∪ (B ∩ A') ∪ (A ∩ B) = [(A ∩ B') ∪ (A ∩ B)] ∪ (B ∩ A') = A ∪ (B ∩ A') = A ∪ B.