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NCERT Class XI Mathematics - Sets - Solutions
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Question : 65 of 73
Marks:
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Show that for any sets A and B, A = (A ∩ B) ∪ (A – B) and A ∪ (B – A) = (A ∪ B)
Solution:
(A ∩ B) ∪ (A – B) = (A ∩ B) ∪ (A ∩ B′) = A ∩ (B ∪ B′) (By distributive law) = A ∩ U = A Hence, A = (A ∩ B) ∪ (A – B) Also A ∪ (B – A) = A ∪ (B ∩ A′) = (A ∪ B) ∩ (A ∪ A′) (By distributive law) = (A ∪ B) ∩ U = A ∪ B Hence, A ∪ (B – A) = A ∪ B.
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