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Math Help - Distributive/Associative Law Q

  1. #1
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    Distributive/Associative Law Q

    If I am trying to prove this:

    For all sets A,B,C
    (A intersection B)\C = (A\C) intersection (B\C)

    If I start with proving X is a subset of Y (L.S. = R.S.), could I do the following?
    (xeA ^ xeB) ^ (x/e/C)
    Then using distributive law...
    (xeA ^ x/e/C) ^ (xeB ^ x/e/C) <=> (A\C) intersection (B\C)

    And then for Y is a subset of X...
    Use the same distributive rule (backwards)

    I'm wondering if this is a justified proof? If not, what would be the correct approach?

    Thanks
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  2. #2
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    Re: Distributive/Associative Law Q

    Quote Originally Posted by DirectorRico View Post
    If I am trying to prove this:
    For all sets A,B,C
    (A intersection B)\C = (A\C) intersection (B\C)

    \begin{align*}(A\cap B)\setminus C&= (A\cap B)\cap C^c\\  &=(A\cap C^c)\cap (B\cap C^c) \\ &=(A\setminus C)\cap(B \setminus C) \end{align*}.
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  3. #3
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    Re: Distributive/Associative Law Q

    Great! Thanks Plato. +rep
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