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A group that is a collection of sets

  1. Oct 20, 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) intersect B) union (A intersect (S-B)).

    Need to show that (P,*) is commutative and the group identity.


    2. Relevant equations



    3. The attempt at a solution

    only attempted to show through venn diagrams..looking for an alternative approach?
     
  2. jcsd
  3. Oct 20, 2009 #2

    lanedance

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    Homework Helper

    unless i'm missing something commutative seems pretty obvious from the definition of the multiplication, jsut re-arrange to show A*B = B*A

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