Owen Z. answered • 04/05/21

Experienced Computer Science and Mathematics Tutor

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).