ABSTRACT
Remember the good and bad news about truth-tables. In theory, we can always use them to check validity in truth-functional logic; but in fact we would often need a table so long or wide, or both, that no one who knew a better way would use that one. And there is a better way: a proof, using rules of inference. ('Infer' here means 'to work out logically'.) In truth-functional logic, our rules can be confirmed by truth-tables; but once we have seen that a rule is acceptable, we can use it without referring back.
