Question

Using properties of sets show that 

(i) A ∪ (A ∩ B) = A 

(ii) A ∩ (A ∪ B) = A. 

Answer 1

(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)  9 = A 

{from (1)}