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Math Help - set property help

  1. #1
    Junior Member
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    set property help

    Am I correct in assuming:

    using A-B = AnB'

    (A-B)-C = (A-C)-B
    (AnB') - C
    (AnB')nC'
    AnB'nC'
    AnC'nB' <- is this legal?
    (A-C)nB'
    = (A-C)-B

    Thanks for any help.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by dunsta View Post
    Am I correct in assuming:

    using A-B = AnB'

    (A-B)-C = (A-C)-B
    (AnB') - C
    (AnB')nC'
    AnB'nC'
    AnC'nB' <- is this legal?
    (A-C)nB'
    = (A-C)-B

    Thanks for any help.
    Yes, that's legal because \cap is commutative ( A\cap B=B\cap A) and associative ( (A\cap B)\cap C=A\cap(B\cap C)).

    Thus, you're correct in saying that

    \begin{aligned}A\cap B^{\prime}\cap C^{\prime}&=A\cap(B^{\prime}\cap C^{\prime})\\ &= A\cap(C^{\prime}\cap B^{\prime})\\ &=(A\cap C^{\prime})\cap B^{\prime}\end{aligned}

    from which the desired result follows.

    Does this make sense?
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  3. #3
    Junior Member
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    Jun 2010
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    Thanks, i like to know I am doing things correctly and not just assuming I am.
    I really appreciate your help and this forum!
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