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If X and Y are two sets and X′ denotes the complement of X, then X ∩ (X ∪ Y)′ is equal to A. XB. Y C. ϕ D. X ∩ Y |
Answer» C. Φ Given: X and Y are two sets To find: X ∩ (X ∪ Y)′ X ∩ (X ∪ Y)′ {∵ A’ ∪ B’ = (A ∩ B)’} = X ∩ (X’ ∩ Y′) = (X ∩ X’) ∩ (X ∩ Y’) = Φ ∩ (X ∩ Y’) {∵ A’ ∩ A = Φ} = Φ {∵ Φ ∩ A = Φ} Hence, X ∩ (X ∪ Y)′= Φ |
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