Modus Tollens

Modus tollens literally means "the mode of denying."

If P, then Q. It is not the case that Q. Therefore, it is not the case that P.

The symbolic form looks like this;

Example. If it is raining, then it is cloudy. It is not cloudy. Therefore, it is not raining.

How does it work? Recall that "necessary" means that whenever the antecedent is present, the it is necessary that the consequent be present. So it logically follows that if the necessary condition (the consequent) is NOT present, that the sufficient condition (the antecedent) couldn't be present either. In our example, you'll remember that there has to be at least a small cloud for there rain, so we know that whenever there are no clouds, then it is guaranteed that there is no rain.

It is called the mode of denying because it denies P by denying Q.