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Math Help - set theory simplification

  1. #1
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    set theory simplification

    \overline{\overline{((A\cup B)}\cap(C))} \cup \overline{(B)}

    I have the first part where you would use demorgans law to break up the a union b and then double negation to cancel the a union b double negation.
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  2. #2
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    Quote Originally Posted by aaronrj View Post
    \overline{\overline{((A\cup B)}\cap(C))} \cup \overline{(B)}

    I have the first part where you would use demorgans law to break up the a union b and then double negation to cancel the a union b double negation.
    It is more convenient to use A' instead of \overline{A}.

    Hence , \overline{\overline{((A\cup B)}\cap(C))} \cup \overline{(B)} = [(A\cup B)'\cap C]'\cup B' = [(A'\cap B')\cap C]'\cup B' = [A\cup B\cup C']\cup B' = (A\cup C')\cup(B\cup B') =  ( A\cup C')\cup E = E

    Where A,B,C are all subsets of E
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