# Arithmetical representation \$F(x,y,z)Longleftrightarrow (x+z)=y lor (y+z)=x\$

I am kind of confused which function $$f:mathbb{N}^2longrightarrowmathbb{N}$$
is presented by $$F(x,y,z)Longleftrightarrow (x+z)=y lor (y+z)=x$$

I know that $$f(x,y)=y-x$$ is represented by $$F(x,y,z)Longleftrightarrow (x+z=y)lor ((z=0)land exists w(x+w)=y)$$

But the or symbol confuses me … My guess was
$$f(x,y)=max{x-y,y-x}$$ but i think this is wrong due to a missing check in F(x,y,z)