are the tools we use to construct proofs. There are two types. The first type is -, which have two distinctive characteristics: each is itself a valid argument form, and they must be applied to whole lines of proof only, never to a component of a statement. The second type is -, which each specify a pair of equivalent terms and allow us to replace any instance of one statement form with the corresponding instance of the other. the rules of implicationthe rules of inferencetruth tablesthe rules of replacement