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Math Help - DeMorgan's law help

  1. #1
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    DeMorgan's law help

    I have this:

    X = ABC + BCD

    (BCD has a not line over it)

    The answer should be:

    X = ABCD

    (X and A have a not line over them)

    Can someone show me the steps to get to the answer?
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  2. #2
    Moo
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    Hello,

    \bar X=(\overline{ABC})(BCD)=(\bar A+\bar B+\bar C)(BCD) =\bar A BCD+\bar B BCD+\bar C BCD=\bar A BCD+(\bar B B)CD+(\bar C C)BD

    Recall that for any P, \bar P P=0, that + and * are associative, etc...
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  3. #3
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    Thanks. I have one more quick question regarding DeMorgan's law.

    Say I have
    \overline{\bar B+\bar C+AD}

    Does it become:
    BC \overline{AD}

    Then:
    (\bar A+\bar D)BC

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  4. #4
    Moo
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    Yes and yes
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