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Help with Set theory please!

  1. Mar 22, 2008 #1
    I was wondering if someone could please look over my proof of this set theory problem and let me know if I am doing it right or not and give me some help.


    Provide a counterexample for the following:

    If (A-B)intersect(A-C)=empty set, then B intersect C = empty set.

    Proof:

    Assume that (A-B)intersect(A-C) does not equal the empty set. Let A={4,26}, B={4,23}, and C={26,23}. Since (A-C)=26 and (A-C)=4, that means that (A-B)intersect(A-C) does not equal the empty set. So B intersect C equals 23 which is also not the empty set.


    Thank you for your help! :smile:
     
  2. jcsd
  3. Mar 22, 2008 #2
    that doesn't quite work, to show

    If (A-B)intersect(A-C)=empty set, then B intersect C = empty set is a false statement, you need to find A, B, C such that (A-B)intersect(A-C)=empty set but B intersect C != empty set
     
  4. Mar 22, 2008 #3
    Ok how about this:

    Proof:

    Let A={4,26}, B={4,23}, and C={26,23}. If (A-C)=26 and (A-C)=4, that means that (A-B)intersect(A-C) equals the empty set. But B intersect C = 23 which is not the empty set, therefore there is a contradiction.

    How is that?
     
  5. Mar 22, 2008 #4
    good work :)

    (I think you mean A-B = {26} though)
     
  6. Mar 22, 2008 #5
    haha got it!


    Thank you!!!!
     
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