1.

For any two sets, prove that:(i) A ∪ (A ∩ B) = A(ii) A ∩ (A ∪ B) = A

Answer»

(i) A ∪ (A ∩ B) = A

As we know union is distributive over intersection

Therefore, A ∪ (A ∩ B)

(A ∪ A) ∩ (A ∪ B) [Here, A ∪ A = A]

A ∩ (A ∪ B)

A

(ii) A ∩ (A ∪ B) = A

As we know union is distributive over intersection

Therefore, (A ∩ A) ∪ (A ∩ B)

A ∪ (A ∩ B) [Here, A ∩ A = A]

A



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