Let predicate $P(t)$ means "student is intelligent"
't' is some person and as for our predicate domain is 'student' so we'll talk when this person belongs to domain 'student'.
$\forall t\in r (P(t))$ will then mean "Every person who is a student is intelligent or simply every student is intelligent"
in other words we can also say it like "there exists no student ($\sim \exists t$) who is dull ($\sim P(t)$)"
$\forall t\in r (P(t))$
$\equiv \sim \sim$( $\forall t\in r (P(t))$ ) //Use one negation to apply Demorgan law
$\equiv \sim \exists t\in r (\sim P(t))$