Let A, B, and C be subsets of a universal set U and suppose n(U) = 200, n(A) = 27, n(B) = 29, n(C) = 33, n(A ∩ B) = 5, n(A ∩ C) = 10, n(B ∩ C) = 13, and n(A ∩ B ∩ C) = 4. Compute:

Question

(a)     n[A ∩ (B ∪ C)]

(b)      n[A ∩ (B ∪ C)^c]

Answer 1

Note that we have A in all answers, so we only need to look at conditions with A.

n(B U C) = n(B) + n(C) - n(BC) Looking within A, we use n(AB) + n(AC) - n(ABC) 5 + 10 - 4 = 11

For the second answer, this is the complement within A.

27 - 11 = 16