For every $x$ and $y$ there exists $z$ such that $x-y=z$

Question

If I have the statement.

For every $x$ and $y$ there exists $z$ such that $x-y=z$

What would the predicate be for that statement? And how would it be written in symbolic notation?

I can't seem to get started.

Answer 1

For every $x$ and $y$ there exists $z$ such that $x−y=z$

$$\forall x~\forall y~\exists z~{(x-y=z)}$$

A predicate is a statement that has a truth value depends on the state of its variables.   The statement that $(x-y=z)$ is a predicate with three variables.