A **deduction rule** allows conversion of true propositions into other true propositions. #### Modus Ponens Modus Ponens: Latin for "Method of affirming" If $A\rightarrow B$ is True and $\neg $ is True, then $\neg A$ is True $(A\rightarrow B) \land A \implies B $ #### Modus Tollens Modus Tollens: Latin for "Method of denying" If $A\rightarrow B$ is True and $A$ is True, then $B$ is True $(A\rightarrow B) \land \neg B \implies \neg A$ #### Chain Syllogism If $A \rightarrow B$ is True and $B \rightarrow C$ is True, then $A \rightarrow C$ is True $(A\rightarrow B) \land (B\rightarrow C) \implies A\rightarrow C $ #### Reductio ad absurdum If $A \rightarrow B$ is True and $A \rightarrow \neg B$ is True, then $\neg A$ is True $(A\rightarrow B) \land (A\rightarrow \neg B) \implies \neg A$ Useful for proof by contradiction