Group that is a collection of sets

[halvizo1031]

Homework Statement

Let S be a set of thing 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)]

Homework Equations

Consider the set S={alice, bob, carol, don, erin, frank, gary, harriot}. Using the set operation * find the subgroup (Q,*) of (P,*) generated by the sets
{alice, bob}, {carol, don}, {erin, frank}, {gary, harriot}.

The Attempt at a Solution

Using the information of b1 how do i solve b2? am i suppose to assume S is Z_8? if so, would S={0,1,2,3,4,5,6,7}?

 

[Office_Shredder]

S is just a set. It's not a group, it's power set is.

So if S has eight elements, your group, P has 2⁸ elements. Trying to figure that group out isn't really the goal of the question though, you should just try multiplying a couple elements of your proposed generating set together and see what happens