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If A and B are two sets, then A ∩ (A ∪ B) equals A. A B. B C. ϕ D. A ∩ B |
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Answer» A. A 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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