# Math Help - De Morgan Rule for Quantifiers

1. ## De Morgan Rule for Quantifiers

$
\neg \forall x \in U[ p(x) ] \equiv \exists x \in U[ \neg p(x) ]
$

$
\neg \exists x \in U[ p(x) ] \equiv \forall x \in U [ \neg p(x) ]
$

Then does this mean,

$
\forall x \in U[ p(x) ] \equiv \neg \exists x \in U[ p(x) ]
$

2. Originally Posted by RedKMan
$
\neg \forall x \in U[ p(x) ] \equiv \exists x \in U[ \neg p(x) ]
$

$
\neg \exists x \in U[ p(x) ] \equiv \forall x \in U [ \neg p(x) ]
$

Then does this mean,

$
\forall x \in U[ p(x) ] \equiv \neg \exists x \in U[ p(x) ]
$
Actually it is $
\forall x \in U[ p(x) ] \equiv \neg \exists x \in U[ \neg p(x) ]
$

BTW: $$x \in U$$ gives $x \in U$.