A morphism is not a binary relation. In a preorder, \$$\le\$$ is a binary relation: for any pair of elements \$$x\$$ and \$$y\$$, \$$x \le y\$$ is either true for false. When \$$x \le y\$$ we can say there's a exactly one morphism from \$$x\$$ to \$$y\$$, if we so desire. But in a general category, there could be many (or no) morphisms \$$f : x \to y\$$.

My remarks on morphisms were aimed only at people who know a bit of category theory and wonder why we're talking about preorders instead. So, if that stuff - or what I just said - makes no sense, don't worry about it too much.