Answer
Universal and Existential Quantification $ \exists x P(x)$: There exists an element $x$ iin the domain such that $\ P(x)$.
Universal Quantitfication $\forall x P(x) $ : $P(x) $ for all values of $x$ in the domain.
$\neg \exists x P(x) \equiv \forall x \neg P(x)$
$\neg \forall x P(x) \equiv \exists x \neg P(x)$
Work Step by Step
Universal and Existential Quantification $ \exists x P(x)$: There exists an element $x$ iin the domain such that $\ P(x)$.
Universal Quantitfication $\forall x P(x) $ : $P(x) $ for all values of $x$ in the domain.
Negation:
$¬p$: not $p$
The negation thus adds the symbol ¬ in front of the expression:
$\neg \exists x P(x)$
$\neg \forall x P(x)$
These statements are also logically equivalent with th following statements using De Morgans laws for Qualifiers:
$\neg \exists x P(x) \equiv \forall x \neg P(x)$
$\neg \forall x P(x) \equiv \exists x \neg P(x)$
