(a.) Find an example of a formula with at least one quantifier that is $\textbf{false}$ when we quantify over the natural numbers $\mathbb{N}$, but $\textbf{true}$ when we quantify over the integer numbers $\mathbb{Z}$.
$(\exists x \in \mathbb{N} : x < 0)\textbf{, False}$
$(\exists x \in \mathbb{Z} : x < 0)\textbf{, True}$
Do this work or is the first one undefined?