1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Question regarding algebra of sets

  1. Aug 30, 2011 #1
    1. The problem statement, all variables and given/known data

    I'm working on a proof for Intro. to Algebra, and the problem deals with proving that the operation of Symmetric Difference imposes group structure on the power set 2^x (set of all subsets) of a given set X. There is a part of my proof that I'd like to get some advice on however...

    I've worked out a proof, and I can see it relies heavily on this equation:

    Let A, B be sets.

    i. A - B = (AuB) - B

    2. Relevant equations

    3. The attempt at a solution

    My proof goes like this: (=>)Let x in A - B. Then, x is in A, implying x is in AuB. Since x cannot be in B, then it also falls in AuB - B.
    (<=): Let x in AuB - B. Then x cannot be in B, and must therefore be in AuB. x not in B but still in AuB - B implies that x must be in A and not in B, which means it also falls in A - B.

    Did I miss anything/ any mistakes?
  2. jcsd
  3. Aug 30, 2011 #2


    User Avatar
    Science Advisor
    Homework Helper

    Sounds fine to me.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook