Actually, it does mean that. If you write out the truth table, A -> B is equivalent to ~A \/ B, which means ~B -> ~A. This is called the contrapositive and is

Actually, it does mean that. If you write out the truth table, A -> B is equivalent to ~A \/ B, which means ~B -> ~A. This is called the contrapositive and is a valid inference. The two classical invalid inferences from A -> B are ~A -> ~B (the inverse) and B -> A (the converse).