Recall that the contrapositive of an implication $p \implies q$ is the equivalent implication $\neg q \implies \neg p$ , which is read: ``not $q$ implies not $p$ ''. The following are examples of the contrapositive and converse of a logical statement:

1. Let $p$ be the statement ``it is raining'' and let $q$ be ``the ground is getting wet''. Then the statement ``if it is raining then the ground is getting wet'' is equivalent to ``if the ground is not getting wet then it is not raining''. Notice that these are both true statements. Notice also that the converse would be ``if the ground is getting wet then it is raining'' (which is not necessarily true!).
2. Let $f:S\to T$ be a function of sets and let $S$ be finite. The contrapositive statement of ``if $f$ is surjective then $T$ is finite'' (a true statement) would be the implication ``if $T$ is not finite then $f$ is not surjective'' (also a true statement). The converse would be ``if $T$ is finite then $f$ is surjective'' (a false statement).