We saw the formal definitions of one-to-one and onto. We looked briefly at the meaning of statements with two unlike quantifiers. Then we did three example proofs: an onto proof for a specific concrete function, a one-to-one proof where one function was defined in terms of another, and the following claim:
Suppose g:A-->B and f:B-->C. Then if fog is one-to-one and g is onto, then f is one-to-one.
Finally, we looked briefly at the pigeonhole principle.