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Math Help - A quick question about carnality of sets

  1. #1
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    Question 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
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  2. #2
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    Re: A quick question about carnality of sets

    when A intersection B is empty. |AUB| = |A| + |B| - |A \intersect B|
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  3. #3
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    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?
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  4. #4
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    Re: A quick question about carnality of sets

    Indeed as coolge said, when you do  |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.
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