The converse of an implication \(P \imp Q\) is the implication \(Q \imp P\text{.}\) The converse is NOT logically equivalent to the original implication. That is, whether the converse of an implication is true is independent of the truth of the implication.
The contrapositive of an implication \(P \imp Q\) is the statement \(\neg Q \imp \neg P\text{.}\) An implication and its contrapositive are logically equivalent (they are either both true or both false).