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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)
Solution
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)]
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