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Math Help - De Morgan Rule for Quantifiers

  1. #1
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    De Morgan Rule for Quantifiers

    <br />
\neg \forall x \in U[ p(x) ] \equiv \exists x \in U[ \neg p(x) ]<br />

    <br />
\neg \exists x \in U[ p(x) ] \equiv \forall x \in U [ \neg p(x) ]<br />

    Then does this mean,

    <br />
\forall x \in U[ p(x) ] \equiv \neg \exists x \in U[ p(x) ]<br />
    Last edited by Plato; March 24th 2010 at 07:01 AM. Reason: LaTeX
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  2. #2
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    Quote Originally Posted by RedKMan View Post
    <br />
\neg \forall x \in U[ p(x) ] \equiv \exists x \in U[ \neg p(x) ]<br />

    <br />
\neg \exists x \in U[ p(x) ] \equiv \forall x \in U [ \neg p(x) ]<br />

    Then does this mean,

    <br />
\forall x \in U[ p(x) ] \equiv \neg \exists x \in U[ p(x) ]<br />
    Actually it is <br />
\forall x \in U[ p(x) ] \equiv \neg \exists x \in U[ \neg p(x) ]<br />

    BTW: [tex]x \in U [/tex] gives x \in U .
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