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Math Help - A Symmtric Difference Question

  1. #1
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    Acolman, Mexico
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    A Symmtric Difference Question

    I have to admit that I am completely lost on this one.

    For any three sets A, B, C, show that A \bigtriangleup B = C if and only if A=B \bigtriangleup C.

    Thanks in advance
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  2. #2
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    Quote Originally Posted by akolman View Post
    I have to admit that I am completely lost on this one.

    For any three sets A, B, C, show that A \bigtriangleup B = C if and only if A=B \bigtriangleup C.

    Thanks in advance

    Hmm...if you already know that the power set of any set is an abelian group of exponent 2 (i.e., an elementary abelian group of exponent 2) wrt the symmetric difference, the result is immediate.

    Otherwise I'm afraid you're going to have to get into nasty union/intersection/difference of sets calculations...

    Tonio
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