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Math Help - Simplifying a Set

  1. #1
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    Simplifying a Set

    Simplify the following using the set rules of interference.

    <br />
[((A - B) \cup (A \cap C)) \cap (A \cap B)^C]^C<br />

    where A, B, and C are subsets of the Universe.



    I've gotten it to (A^C \cup (B \cap C^C)) \cup (A \cap B), but now I'm stuck.

    Could anyone please help out?


    Thanks!
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  2. #2
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    Quote Originally Posted by inferno View Post
    Simplify the following using the set rules of interference.

    <br />
[((A - B) \cup (A \cap C)) \cap (A \cap B)^C]^C<br />

    where A, B, and C are subsets of the Universe.



    I've gotten it to (A^C \cup (B \cap C^C)) \cup (A \cap B), but now I'm stuck.

    Could anyone please help out?


    Thanks!
    I am going to use the dash notation instead of the "c" natation,so:


    [((A - B) \cup (A \cap C)) \cap (A \cap B)^C]^C = <br />
[((A - B) \cup (A \cap C)) \cap (A \cap B)']' = [((A - B) \cup (A \cap C))' \cup (A \cap B)]

    All you have to do now is to simplify [((A - B) \cup (A \cap C))']
    Last edited by xalk; February 24th 2010 at 03:52 AM. Reason: not finished the post
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  3. #3
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    xalk, thanks for your help. I realized that I needed to use the commutative and associative laws and then the absorption laws to arrive at an answer of an union of two subsets.
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