I've been working on this problem for a while. Could someone show me how to connect the last part?
Let A, B, and C be finite sets. Prove:
If
then A, B, and C must be pairwise disjoint.
Here is what I have:
Suppose A, B, and C are finite sets with .
By inclusion/exclusion, we know that
By cancellation, we have:
I'm just not sure how to connect that to "Thus A, B, and C must be pairwise disjoint."