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: Joseph is not playing a game. If it rains, then Jennifer is a taxi driver. If Jennifer were a taxi driver, then Joseph is playing a game. If Joseph plays a game, then Jennifer is a taxi driver. Jennifer is a taxi driver if and only if it is raining.
Jennifer is not a taxi driver can be inferred via the modus tollens rule. If it rains, then Joseph is playing a game can be inferred via the transitivity rule. Jennifer is a taxi driver if and only if Joseph is playing a game can be inferred via the biconditional introduction rule. Joseph is playing a game if and only if Jennifer is a taxi driver can be inferred via the biconditional introduction rule. If Jennifer were a taxi driver, then it is raining can be inferred via the biconditional elimination rule. If it rains, then Jennifer is a taxi driver can be inferred via the biconditional elimination rule.