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U is a universal set and n (U) = 160. A, B and C are subset of U. If n(A) = 50, n(B) = 70, n(B ∪ C) = ϕ , n(B ∩ C) = 15 and A ∪ B ∪ C = U, then n (C) equals. (a) 40 (b) 50 (c) 55 (d) 60 |
Answer» (c) 55 A ∪ B ∪ C = U and A ∩ (B ∪ C) = ϕ ⇒ (B ∪ C) = A′= U – A ⇒ n (B ∪ C) = n (U) – n (A) = 160 – 50 = 110 Now, n (B ∪ C) = n (B ) + n (C) – n (B ∩ C) ⇒ 110 = 70 + n (C) – 15 ⇒ n (C) = 110 + 15 – 70 = 55. |
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