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Homework Help: Group that is a collection of sets

  1. Oct 21, 2009 #1
    1. The problem statement, all variables and given/known data
    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)]

    2. Relevant 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}.

    3. 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}?
  2. jcsd
  3. Oct 21, 2009 #2


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    Staff Emeritus
    Science Advisor
    Gold Member

    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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