Sets · Class 11 · CBSE · Science Mathematics
For subsets A and B of a universal set U, prove that (A ∪ B)′ = A′ ∩ B′.
Practice question from Sets (Class 11 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.
hard · Subjective · Q-8250B6
For subsets A and B of a universal set U, prove that (A ∪ B)′ = A′ ∩ B′.
Answer: Let x be any element of U. Then x ∈ (A ∪ B)′ if and only if x ∉ A ∪ B, which means x ∉ A and x ∉ B. Hence, x ∈ A′ ∩ B′, so (A ∪ B)′ = A′ ∩ B′.
Solution
An element is in the complement of exactly when it belongs to neither A nor B. This is precisely the condition for belonging to , proving the identity.
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