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 ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

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}

B ∩ C = {4,5,6}  
∴ A ∪ (B ∩ C) = {1, 2, 3, 4, 5, 6}             ...(i)
A ∪ B = {1, 2, 3, 4, 5, 6}
(A ∪ C) = {1, 2, 3, 4, 5, 6, 7, 8}
∴ (A ∪ B) ∩ (A ∪ C) = {1, 2, 3, 4, 5, 6}   ...(ii)
From (i) and (ii), we get
A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)