Consider the following premises. It is not overcast. Robert is happy if and only if it is overcast. If Jessica cooks, then Robert is happy. If Robert were happy, then Jessica is cooking. Can we infer the following from them? If we can, name the inference rule being used: Jessica is not cooking.
 From the fact that if Robert were happy, then Jessica is cooking, and that if Jessica cooks, then Robert is happy we can infer that Robert is happy if and only if Jessica is cooking via biconditional introduction. From the fact that Robert is happy if and only if it is overcast we can infer that if Robert were happy, then it is overcast via biconditional elimination. From the fact that if Robert were happy, then it is overcast, and that it is not overcast we can infer that Robert is not happy via modus tollens. Finally, from the fact that Robert is happy if and only if Jessica is cooking, and that Robert is not happy we can infer that Jessica is not cooking via biconditional elimination. Therefore, the answer is yes.