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Question
Show that for any sets A and B, A = (A ∩ B) ∪ ( A - B)
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Solution
Right side = (A ∩ B) ∪ (A – B)
= (A ∩ B) ∪ (A ∩ B) [∴ A – B = A ∩ B’]
= (A ∩ (B ∪ B') (by distributive property)
= A ∩ U (here U is the universal set)
Hence, (A ∩ B) (A – B)
= A.
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