Question

If A, B, C are the sets for the letters in the words 'college', 'marriage' and 'luggage' respectively, then verify that
A - (B ∪ C) = (A - B) ∩ (A - C)

Answer 1

A = {c, o, l, g, e}

B = {m, a, r, i, g, e}

C = {l, u, g, a, e}

B ∪ C = {m, a, r, i, g, e, l, u}

A - (B ∪ C) = {c, o}

A - B = {c, o, l}

A - C = {c , o}

∴ [(A - B) ∩ (A - C)] = {c , o} = A - (B ∪ C)

∴ [A - (B ∪ C)] = [(A - B) ∩ (A - C)]