I'm trying to write the definition of a one-one and onto functions using logical quantifiers. Is the following correct:

Let f be a function from S to W.

One-one:

If f(s) = w then for all s' in S such that s' != s, f(s') != t.

Onto:

For all w in W, there exists at least one s in S such that f(s) = w.

I'm pretty sure about what I've written for onto, but not about one-one. Thanks for helping me clarify these simple concepts.