Modus Tollens

## Modus Tollens

 Definition: Let $P$ and $Q$ be statements. Then the rule of inference known as Modus Tollens is given by the argument $((P \rightarrow Q) \wedge \neg Q) \rightarrow \neg P$.

For example, let $P$ and $Q$ be the following statements:

• $P$: Bob has studied for the test.
• $Q$: Bob will pass the test.

Then Modus Tollens say that if Bob studying for the test means that Bob will pass the test and Bob does not pass the test then Bob did not study for the test.