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Math Help - Basic proof

  1. #1
    Junior Member
    Joined
    Feb 2009
    Posts
    33

    Basic proof

    I need to prove that A-B = A - (A\cap B)

    Using a Venn diagram, this proof is so trivial but how do I prove this mathematically?

    So far I have
    A-B = A\cap B^{C}
    =A\cap(S-B) where S is the sample space

    But now I'm stuck...
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  2. #2
    Senior Member
    Joined
    Nov 2008
    From
    Paris
    Posts
    354
    Hi

    You can prove it with two inclusions. One is quite simple:

    A-B\subseteq A-(A\cap B)\ . Do you see why?

    Then take x\in A-(A\cap B). What does it mean for x?
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