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: It is cloudy if and only if it is raining. It is cloudy or Joseph is rich. Sarah is cooking if and only if it is raining. Sarah is not cooking.
If it is cloudy, then it is raining can be inferred via the biconditional elimination rule. If Sarah cooks, then it is raining can be inferred via the biconditional elimination rule. If it rains, then it is cloudy can be inferred via the biconditional elimination rule. If it rains, then Sarah is cooking can be inferred via the biconditional elimination rule. It is not raining can be inferred via the biconditional elimination rule.