Let A, B, and C be subsets of a universal set U

Question

Let A, B, and C be subsets of a universal set U and suppose n(U) = 200,n(A) = 23, n(B) = 25, n(C) = 29, n(A ∩ B) = 8, n(A ∩ C) = 9, n(B ∩ C) = 16,and n(A ∩ B ∩ C) = 6. Compute:

(a)     n[A ∩ (B ∪ C)]

 

(b)      n[A ∩ (B ∪ C)^c]

Answer 1

a) n(A ∩(B ∪ C))= n((A∩B) ∪ (A∩C)) = n(A∩B) + n(A∩C) - n((A∩B)∩(A∩C)) = n(A∩B) + n(A∩C) - n(A∩B∩C) =8+9-6 = 11

b) n(A∩(B∪C)') = n(A) - n(A ∩(B ∪ C)) = 23 - 11 = 12