Consider the following premises. Susan is running if and only if it is overcast. If Sarah cooks, then it is overcast. If it is overcast, then Sarah is cooking. Can we infer the following from them? If we can, name the inference rule being used: The fact that Sarah cooks does not imply that Susan is running.
 From the fact that if it is overcast, then Sarah is cooking, and that if Sarah cooks, then it is overcast we can infer that it is overcast if and only if Sarah is cooking via biconditional introduction. From the fact that it is overcast if and only if Sarah is cooking we can infer that if Sarah cooks, then it is overcast via biconditional elimination. From the fact that Susan is running if and only if it is overcast we can infer that if it is overcast, then Susan is running via biconditional elimination. Finally, from the fact that if Sarah cooks, then it is overcast, and that if it is overcast, then Susan is running we can infer that if Sarah cooks, then Susan is running via transitivity, which contradicts that The fact that Sarah cooks does not imply that Susan is running. Therefore, the answer is no.