NCERT Class XI Mathematics - Sets - Solutions
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Question : 66
Total: 73
Using properties of sets, show that
(i) A ∪ (A ∩ B) = A (ii) A ∩ (A ∪ B) = A.
(i) A ∪ (A ∩ B) = A (ii) A ∩ (A ∪ B) = A.
Solution:
(i) We know that if A ⊂ B, then
A ∪ B = B. Also, A ∩ B ⊂ A \ A ∪ (A ∩ B) = A.
(ii) We know that if A ⊂ B, then A ∩ B = A Also, A ⊂ A ∪ B
∴ A ∩ (A ∪ B) = A.
A ∪ B = B. Also, A ∩ B ⊂ A \ A ∪ (A ∩ B) = A.
(ii) We know that if A ⊂ B, then A ∩ B = A Also, A ⊂ A ∪ B
∴ A ∩ (A ∪ B) = A.
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