Help please I don't know how to solve

Question

Let A, B, and C be subsets of a universal set U and suppose n(U) = 100, n(A) = 26, n(B) = 28, n(C) = 32, n(A ∩ B) = 6, n(A ∩ C) = 9, n(B ∩ C) = 14, and n(A ∩ B ∩ C) = 4. Compute:

 n[A ∩ (B ∪ C)]

 

  n[A ∩ (B ∪ C)^c]

Can someone help me solve this I keep getting 15 and 28 I don't know what im doing wrong

Answer 1

My video shows how to get the correct solution, but I want to address why some of what you got was incorrect.

Presumably, you got 15 by doing n(A∩C)+n(A∩B). The problem here is some elements are in both sets, and so you count them twice. To fix this, you need to subtract 1 for each element you double counted. That’s as simple as subtracting where the two sets intersect: (A∩C)∩(A∩B), or simply (A∩B∩C).

Simply put n(X∪Y) = n(X) + n(Y) - n(X∩Y).