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»

L.H.S = 

(B ∩ C) = {x:x ϵ B and x ϵ C} 

= {5, 6} 

A ∪ (B ∩ C) = {x: x ϵ A or x ϵ (B ∩ C) } 

= {1, 2, 4, 5, 6}. 

R.H.S = 

(A ∪ B) = {x: x ϵ A or x ϵ B } 

= {1, 2, 4, 5, 6}. 

(A ∪ C) = {x: x ϵ A or x ϵ C } 

= {1, 2, 4, 5, 6, 7}. 

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

= {1, 2, 4, 5, 6}. 

Hence Verified.



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