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 = {3, 4}

∴ (A ∩ B)' = {1, 2, 5, 6, 7, 8, 9, 10}   …(i)

A' = {5, 6, 7, 8, 9, 10}

B' = {1, 2, 7, 8, 9, 10}

∴ A' ∪ B' = {1, 2, 5, 6, 7, 8, 9, 10}    ...(ii)

From (i) and (ii), we get

(A ∩ B)' = A' ∪ B'