Law of contrapositive

The law of contrapositive states that, in a conditional, if the conclusion is false, then the hypothesis must be false also. The general form is the following:

1. P→Q
2. ~Q
3. Therefore we can conclude ~P.

The following are examples:

1. If it is raining, then there are clouds in the sky.
2. There are no clouds in the sky.
3. Thus, it is not raining.