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Question regarding algebra of sets

  1. Aug 30, 2011 #1
    1. The problem statement, all variables and given/known data

    I'm working on a proof for Intro. to Algebra, and the problem deals with proving that the operation of Symmetric Difference imposes group structure on the power set 2^x (set of all subsets) of a given set X. There is a part of my proof that I'd like to get some advice on however...

    I've worked out a proof, and I can see it relies heavily on this equation:

    Let A, B be sets.

    i. A - B = (AuB) - B

    2. Relevant equations

    3. The attempt at a solution

    My proof goes like this: (=>)Let x in A - B. Then, x is in A, implying x is in AuB. Since x cannot be in B, then it also falls in AuB - B.
    (<=): Let x in AuB - B. Then x cannot be in B, and must therefore be in AuB. x not in B but still in AuB - B implies that x must be in A and not in B, which means it also falls in A - B.

    Did I miss anything/ any mistakes?
     
  2. jcsd
  3. Aug 30, 2011 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Sounds fine to me.
     
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