# A quick question about carnality of sets

• Nov 25th 2012, 06:33 AM
foreverwaiting
A quick question about carnality of sets
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
Thank you
• Nov 25th 2012, 06:53 AM
coolge
Re: A quick question about carnality of sets
when A intersection B is empty. |AUB| = |A| + |B| - |A \intersect B|
• Nov 25th 2012, 07:12 AM
foreverwaiting
Re: A quick question about carnality of sets
Thank you. If that's the case, then when is |A n B| = |A| + |B|?
Would it be when A u B is empty?
• Nov 25th 2012, 07:12 AM
jakncoke
Re: A quick question about carnality of sets
Indeed as coolge said, when you do \$\displaystyle |A \cup B| \$ 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.