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Math Help - Discrete Math - Cardinals

  1. #1
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    Discrete Math - Cardinals

    I need to prove this:

    if |A\B|=|B\A| then |A|=|B|

    The only thing I can see is that this means that I can create a surjective (onto) +injective (one-to-one) function from A to B.

    How can I continue solving this?

    Thank you very much !
    Last edited by mr fantastic; August 13th 2009 at 04:33 PM.
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  2. #2
    Super Member Gamma's Avatar
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    what are A and B? Are these sets? Numbers? is || cardinality of sets or absolute value? If they are sets what do you mean A/B are these cosets or what? As it stands your question makes 0 sense to me.
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  3. #3
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    A and B are sets. the meaning of | | is cardinality of sets.

    A\B is defined as: A ∖ B = A ∩ Bc (c is complement)
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  4. #4
    Super Member Gamma's Avatar
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    |A-B|=|A|-|A\cap B|
    |B-A|=|B|-|B \cap A|

    If these are the same and we subtract, we get 0 on the LHS and clearly A\cap B=B\cap A \Rightarrow |A\cap B|=|B\cap A|

    0=|A|-|B|\Rightarrow |A|=|B|
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  5. #5
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    Well I really appreciate your good wish to help, but since I posted this on the wrong forum I really couldn't expect to recieve the most percise answers for my problem.

    After posting this on the right forum, I got a more percise answer which included ways of solving it that are in my studying material.

    Thank you very much anyway
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