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A group that is a collection of sets

  • #1

Homework Statement


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.


Homework Equations





The Attempt at a Solution



only attempted to show through venn diagrams..looking for an alternative approach?
 

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
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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