I've got a homework question. I am confused with the two variables $x$ and $y$.
In the domain of integers, consider the following predicates: Let $N(x)$ be the statement "$x \ne 0$." Let $P(x, y)$ be the statement "$xy = 1$."
Translate the following statement into the symbols of predicate logic:
For all integers $x$, there is some integer $y$ such that if $x \ne 0$, then $xy = 1$.
This is what I have, not sure if it's right:
$(\forall x)(\exists y)(N(x) \to P(x,y))$