when A intersection B is empty. |AUB| = |A| + |B| - |A \intersect B|
I can't figure this out, it seems almost like a trick question.
When is |A u B| = |A| + |B|?
I'm not even sure what type of answer my professor is looking for so I've been working with quantifiers.
Using quantifiers the closest to the correct answer I can come up with is something like this:
|A u B| = |A| + |B| when "for all"x(x is an element of A and x is an element of B), but it still doesn't satisfy the problem
Indeed as coolge said, when you do the intersection only gets counted once, but |A| + |B|, would mean the intersection gets counted twice. So they are equal precisely when there is nothing in the intersection.