What is a contrapositive proof?

[mysteryman]

Selecting an appropriate proof method is often the hard part.  I usually choose contrapositive proof primarily as a way of converting a "for every..." statement into a "for at least one..." statement (which is thus usually easier to prove), as you demonstrate in your example.  Am I thinking along the right lines?

[chuckjls]

If you prove ~B implies ~A, does ~A imply ~B? I think I remember that it is not true. But I have forgotten why.