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

I am kind of confused which function $$f:\mathbb{N}^2\longrightarrow\mathbb{N}$$ 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)