If A, B, C are the sets for the letters in the words ‘college’, �

1.	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» 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)]

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»

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)]