1.

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identities: A ∩ (B – C) = (A ∩ B) – (A ∩ C)

Answer»

B–C is defined as {x ϵ B : x ∉ C} 

B = {2, 3, 5, 6} 

C = {4, 5, 6, 7} 

B–C = {2, 3} 

(A ∩ (B – C)) = {x:x ϵ A and x ϵ (B – C)} 

= {2} 

R.H.S: 

(A ∩ B) = {x:x ϵ A and x ϵ B} 

= {2, 5} 

(A ∩ C) = {x:x ϵ A and x ϵ C} 

= {4, 5} 

(A ∩ B) – (A ∩ C) is defined as {x ϵ (A ∩ B) : x ∉ (A ∩ C)} 

= {2}. 

Hence Verified.



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