Question

Let A = {1,2,4,5}, B = {2,3,5,6}, C = {4,5,6,7} verify the following identity 

A ∪ (B∩C) = [(A ∪ B) ∩ (A ∪ C)]

Answer 1

L.H.S = A ∪ (B ∪ C) 

= {1,2,3,4,5} ∪ [{2,3,5,6} ∩ {4,5,6,7}] 

= {1,2,4,5} ∪ {5,6} 

= {1,2,4,5,6} 

R.H.S = (A ∪ B) ∩ (A ∪ C) 

= [{1,2,4,5} ∪ {2,3,5,6}] ∩ [{1,2,4,5} ∪ {4,5,6,7}] 

= {1,2,3,4,5,6} ∩ {1,2,4,5,6,7}

= {1,2,4,5,6} 

∴ L.H.S = R.H.S