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Math Help - Set theory help please!

  1. #1
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    Set theory help please!

    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!
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  2. #2
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    Quote Originally Posted by calcprincess88 View Post
    Provide a counterexample for the following:
    If (A-B)intersect(A-C)=empty set, then B intersect C = empty set.
    Proof:
    Assume
    You are not doing a proof, you are giving a counterexample to show that the statement is false.
    This is the way it is done. Find a specific example such as: A={1,2,3}, B={1,2} & C={2,3}.
    Now show that those sets satisfy the hypothesis (the if part) but fail to satisfy the conclusion (the then part). Do not assume anything beyond the example you choose..
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