Consider the statement
$$\forall n \in \mathbb{Z}, \ [E(n) \rightarrow \exists k \in \mathbb{Z} \ (n = 2k \wedge E(k))],$$
where E(x) denotes "x is even." This asserts: "For every integer n, if n is even then there exists an integer k such that n = 2k and k is even." Write the negation of this statement in symbolic form, simplify it, and explain in words what the negation means.