Question 9:

Using properties of sets show that 

(i) A ∪ (A ∩ B) = A

(ii) A ∩ (A ∪ B) = A.

Answer

(i) To show: A ∪ (A ∩ B) = A

We know that

A ⊂ A

A ∩ B ⊂ A

 ∴ A ∪ (A ∩ B) ⊂ A … (1)

Also,   A ⊂ A ∪ (A ∩ B) … (2)

∴ From (1) and (2), A ∪ (A ∩ B) = A

(ii) To show: A ∩ (A ∪ B) = A

A ∩ (A ∪ B) = (A ∩ A) ∪ (A ∩ B)

= A ∪ (A ∩ B)

= A {from (1)}

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