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 an office clerk. Robert is not a sailor. If Mary were a politician, then Robert is a sailor. Joseph is an office clerk if and only if it is cloudy.
Mary is not a politician can be inferred via the modus tollens rule. Joseph is not an office clerk and Robert is not a sailor can be inferred via the conjunction rule. Robert is not a sailor and Joseph is not an office clerk can be inferred via the conjunction rule. If Joseph were an office clerk, then it is cloudy can be inferred via the biconditional elimination rule. If it is cloudy, then Joseph is an office clerk can be inferred via the biconditional elimination rule. It is not cloudy can be inferred via the biconditional elimination rule.