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: Thomas is not sleeping. Thomas is sleeping if and only if Susan is a politician. Joseph is not a lawyer. Joseph is a lawyer if and only if Charles is playing a game.
Thomas is not sleeping and Joseph is not a lawyer can be inferred via the conjunction rule. Joseph is not a lawyer and Thomas is not sleeping can be inferred via the conjunction rule. If Thomas sleeps, then Susan is a politician can be inferred via the biconditional elimination rule. If Joseph were a lawyer, then Charles is playing a game can be inferred via the biconditional elimination rule. If Susan were a politician, then Thomas is sleeping can be inferred via the biconditional elimination rule. If Charles plays a game, then Joseph is a lawyer can be inferred via the biconditional elimination rule. Susan is not a politician can be inferred via the biconditional elimination rule. Charles is not playing a game can be inferred via the biconditional elimination rule.