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)' = (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 ∪ B = {1, 2, 3, 4, 5, 6}
∴ (A ∪ B)' = {7, 8, 9, 10}    ...(i)
A' = {5, 6, 7, 8, 9, 10},
B' = {1, 2, 7, 8, 9, 10}
∴ A' ∩ B' = {7, 8, 9, 10}     ...(ii)
From (i) and (ii), we get
(A ∪ B)' = (A'∩ B')