A group that is a collection of sets

[halvizo1031]

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?

 

[lanedance]

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

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