What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: If James were a taxi driver, then Mary is working. Joseph is not a politician. If Richard plays a game, then Joseph is a politician. If Mary works, then James is a taxi driver. If James were a taxi driver, then Richard is playing a game.
Richard is not playing a game can be inferred via the modus tollens rule. If Mary works, then Richard is playing a game can be inferred via the transitivity rule. If James were a taxi driver, then Joseph is a politician can be inferred via the transitivity rule. James is a taxi driver if and only if Mary is working can be inferred via the biconditional introduction rule. Mary is working if and only if James is a taxi driver can be inferred via the biconditional introduction rule.