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: James is working if and only if it is late. If Joseph sleeps, then it is late. Joseph is not sleeping. If it is late, then Joseph is sleeping.
It is not late can be inferred via the modus tollens rule. Joseph is sleeping if and only if it is late can be inferred via the biconditional introduction rule. It is late if and only if Joseph is sleeping can be inferred via the biconditional introduction rule. If James works, then it is late can be inferred via the biconditional elimination rule. If it is late, then James is working can be inferred via the biconditional elimination rule.