# Law of composition

I understood up to now that the term 'law of composition' was an older alternative to 'binary operation'. But according to this Wikipedia disambiguation page it is an alternative to 'binary function'. Which is correct? Also, which term is preferred, out of 'law of composition' and 'binary operation', if any?

-
Both functions and relations can be composed (see en.wikipedia.org/wiki/Function_composition - there's a paragraph about relations), as long domains and codomains match: if $f: X \to Y$ and $g: Y \to Z$, then $g \circ f: X \to Z$. $f, g$ can be interpreted as either functions in $\bf Set$ or relations in $\bf Rel$ –  alancalvitti Jan 25 '13 at 13:12