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Homework Help: A - B = B - A only if A = B

  1. Feb 5, 2009 #1
    1. The problem statement, all variables and given/known data

    For what conditions on sets A and B does A-B = B-A hold?

    2. Relevant equations

    A - B = A n B^c
    B - A = B n A^c

    3. The attempt at a solution

    I know that A = B is the answer, but I just don't know where to start...please don't give me the whole proof, I want to figure it out myself. I just need a hint or an idea of where to start.
  2. jcsd
  3. Feb 5, 2009 #2


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    Staff Emeritus
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    Gold Member

    Start with: If A=B, show A-B = B-A (this should be easy)

    Then suppose A-B = B-A. If [tex]a \in A[/tex] you need to prove [tex]a \in B[/tex] and vice versa (the vice versa part comes immediately from the symmetry of the problem if you want to be suave about it)
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