1.

For any sets A and B show that (i) (A ∩ B) ∪ (A – B) = A (ii) A ∪ (B - A) = A ∪ B

Answer»

(i) (A ∩ B) ∪ (A – B) = A 

L.H.S = (A ∩ B) ∪ (A – B) 

= (A ∩ B) ∪ (A – B’) [∴ (A – B) = (A – B’] 

= A ∩ (B ∪ B’)      [By distributive law] 

= A ∩ (U)      [(B υ B') = U =Universal set] 

= A 

= R.H.S 

(ii) A ∪ (B - A) = A ∪ B 

L.H.S = A ∪ (B - A) 

= A ∪ (B – A’) [∴ (B - A) = (B ∩ A’] 

= (A ∪ B) ∩ (A ∪ A’)      [By distributive law] 

= (A ∪ B) ∩ U 

= A ∪ B      [∴ A υ A' = U =Universal set] 

= R.H.S



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