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 ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

B ∪ C = {3, 4, 5, 6, 7, 8}

∴ A ∩ (B ∪ C) = {3, 4}            ...(i)

A ∩ B = {3, 4}

A ∩ C = {4}

∴ (A ∩ B) ∪ (A ∩ C) = {3, 4}   ...(ii)

From (i) and (ii), we get

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)