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Math Help - Need some help

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    5

    Need some help

    Prove or disprove

    For all sets A and B:

    If B ⊆ A^c, then A n B = ∅
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  2. #2
    Super Member Gamma's Avatar
    Joined
    Dec 2008
    From
    Iowa City, IA
    Posts
    517

    True

    suppose not. Then there would be an x\in B \cap A. But this means x is in A and x is in B. But since x is in B, and B \subset A^c, then x is in the complement of A. But then we have x\in A^c and x \in A, which is clearly a contradiction as A \cap A^c = \emptyset
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