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 Elisabeth cooks, then it is raining. It is overcast if and only if Elisabeth is cooking. It is not raining. If it rains, then Elisabeth is cooking.
Elisabeth is not cooking can be inferred via the modus tollens rule. Elisabeth is cooking if and only if it is raining can be inferred via the biconditional introduction rule. It is raining if and only if Elisabeth is cooking can be inferred via the biconditional introduction rule. If it is overcast, then Elisabeth is cooking can be inferred via the biconditional elimination rule. If Elisabeth cooks, then it is overcast can be inferred via the biconditional elimination rule.