1.

Using properties of sets and their complements prove that:(i) (A ∪ B) ∩ (A ∩ B’) = A (ii) A - (A ∩ B) = A – B

Answer»

(i) (A ∪ B) ∩ (A ∩ B’) = A 

L.H.S = (A ∪ B) ∩ (A ∩ B’) 

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

= A ∪ ∅             (∴ B ∩ B’ = ∅) 

= A 

R.H.S. 

(ii) A - (A ∩ B) = A – B 

L.H.S = A - (A ∩ B) 

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

= A ∩ (A’ ∪ B)’           (By Demorgan's law) 

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

= ∅ ∪ A ∩ B’             (∴ A ∩ A’ = ∅) 

= A ∩ B’ 

= A – B 

= R.H.S



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