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A group that's a collection of sets

  1. Oct 21, 2009 #1
    1. The problem statement, all variables and given/known data
    Let S be a set of things and let P be the set of subsets of S. For A,B in P, define
    A*B=[(S-A)intersection B] union [A intersection (S-B)]
    I'm suppose to show that (p,*) is commutative, find the identity, and given that A is a subset of S, find the inverse of A. How do i even start this?



    2. Relevant equations



    3. The attempt at a solution
    I need help starting it.
     
  2. jcsd
  3. Oct 21, 2009 #2
    Show that [tex]A*B=B*A[/tex].

    Find [tex]I \in S[/tex] such that [tex]A*I=I*A=A , \quad\forall A \in P[/tex].

    Find [tex]B \in S[/tex] such that [tex]A*B=I [/tex].
     
  4. Oct 21, 2009 #3

    lanedance

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    did you try what i suggested in your last post? (the exact same question)

    https://www.physicsforums.com/showthread.php?t=347210

    it was also suggested to use the fact unions & intersections are commutative operations
     
  5. Oct 21, 2009 #4

    I'm sorry but i couldn't understand what you wrote. And by that i mean that i cant read it. Could you rewrite it please?
     
  6. Oct 21, 2009 #5

    lanedance

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    then try the follwing multiplications: A with the empty set & A with its complement
     
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