Question

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 1

(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.