1. Not finding help here? Sign up for a free 30min 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!

Symmetric difference proof

  1. Nov 14, 2012 #1
    1. The problem statement, all variables and given/known data

    Let % be the symmetric difference.
    Prove that for any sets A, B, C;

    A%B=C iff B%C=A iff A%C=B

    2. Relevant equations

    (I will use forwardslash as I cannot find the backslash on my keyboard.)

    3. The attempt at a solution

    Take x in A%B. Then x is either in A/B or in B/A and in C. Choose the former. Then x is in A and x is in C which implies x is in AnC. This is what I know.
    Now, using these I will prove that B%C=A.
    Take x in (B/C)U(C/B). Then x is either in the first or in the second. Actually it cannot be in the first because that would imply that x is not in C, which contradicts that x is in C. So x is in C/B. But I already know that x is in A, so nothing to prove in that direction. Take x in A... I don't know how to proceed.
     
  2. jcsd
  3. Nov 14, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi bedi! :smile:
    (to prove from left to right …)

    you need to start "B%C = B%(A%B) = … " :wink:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Symmetric difference proof
Loading...