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Group that is a collection of sets

  • #1

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}?
 

Answers and Replies

  • #2
Office_Shredder
Staff Emeritus
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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
 

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