Question

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
A = (A ∩ B) ∪ (A ∩ B')

Answer 1

A = {1, 2, 3, 4},
B = {3, 4, 5, 6},
C = {4, 5, 6, 7, 8} 
X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {1, 2, 3, 4}                               …(i)
A ∩ B = {3, 4}
B' = {1, 2, 7, 8, 9, 10}
A ∩ B' = {1, 2}
∴ (A ∩ B) ∪ (A ∩ B') = {1, 2, 3, 4} …(ii)
From (i) and (ii), we get
A = (A ∩ B) ∪ (A ∩ B')