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Math Help - Set operations

  1. #1
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    Set operations

    for all sets, A B and C.

    is this statement true?

    (A - B) - C = A - (B - C)
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by brudman View Post
    for all sets, A B and C.

    is this statement true?

    (A - B) - C = A - (B - C)
    Note that \left(A-B\right)-C=\left(A\cap B^{\prime}\right)\cap C^{\prime}. Since we're dealing with intersections, we see that

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

    So it appears that \left(A-B\right)-C\neq A-\left(B-C\right) (this is reasonable, because "subtraction" isn't associative).

    Does this make sense?
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  3. #3
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    yes it does, thank you
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  4. #4
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    BTW.
    If I were your professor, I would expect you to give a counter-example.
    That is the proper method of showing a statement is false.
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  5. #5
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    This isn't a question from my professor, i just wanted to know if it is true or not
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