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Using properties of sets, show that (i) A∪(A∩B) = A (ii) A∩(A∪B) = A

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Using properties of sets, show that

(i) A∪(A∩B) = A

(ii) A∩(A∪B) = A

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(i) A ∪ (A ∩ B) = (A ∪ A) ∩ (A ∪ B) 

∵ distributive law = A ∩ (A ∪ B) = A 

(ii) A ∩ (A ∪ B) = (A ∩ A) ∪ (A ∩ B) 

∵ distributive law = A ∪ (A ∩ B) = A.

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