The Law of Syllogism

## The Law of Syllogism

Definition: Let $P$, $Q$, and $R$ be statements. Then the rule of inference known as The Law of Syllogism is given by the argument $((P \rightarrow Q) \wedge (Q \rightarrow R)) \rightarrow \neg R$. |

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

- $P$: Bob has studied for the test.

- $Q$: Bob will pass the test.

- $R$: Bob will pass his class.

Then the law of syllogism states that if Bob has studies for his test implies that Bob will pass his test and if Bob passing his test implies that Bob will pass his class then Bob studying for his test implies that Bob will pass his class.