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Math Help - Venn Diagram proof?

  1. #1
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    Venn Diagram proof?

    Proof for all sets A, B, and C:
    A complement Union B complement = (A Intercept B) complement.

    can someone help??
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  2. #2
    Behold, the power of SARDINES!
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    Note: to show that two set are equal we need to show

    (A^c \cup B^c) \subset (A \cap B)^c and (A \cap B)^c  \subset (A^c \cup B^c)

    let x \in (A^c \cup B^c) by definition

    x \in A^c \mbox{ or } x \in B^c by negation

    x \notin A \mbox{ and } x \notin B by definition

    x \notin (A \cap B) (def of compliment) Since x is not in A and B it must be in

    x \in (A \cap B)^c

    This is half the proof Now you need to show the 2nd part.

    Good luck

    P.s. I think this is one form of DeMorgans Law.
    Last edited by TheEmptySet; March 15th 2008 at 07:25 PM.
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