Answer
∼(∀x ∈ D(∀y ∈ E(P(x, y))))
$\equiv$ ∃x ∈ D(∼(∀y ∈ E(P(x, y))))
$\equiv$ ∃x ∈ D(∃y ∈ E(∼P(x, y)))
Work Step by Step
Recall the negation of a for all statement:
~($\forall x$ in D, P(x)) $\equiv$ $\exists x$ in D such that ~P(x).
To negate a multiply quantified statement, apply the laws from in stages moving left to right along the sentence.
