Consider the following premises. If it is cloudy, then it is not windy. Thomas is cooking. If James were rich, then Thomas is not cooking. It is windy. Can we infer the following from them? If we can, name the inference rule being used: It is not cloudy and James is not rich.
 From the fact that if it is cloudy, then it is not windy, and that it is windy we can infer that it is not cloudy via modus tollens. From the fact that if James were rich, then Thomas is not cooking, and that Thomas is cooking we can infer that James is not rich via modus tollens. Finally, from the fact that it is not cloudy, and that James is not rich we can infer that it is not cloudy and James is not rich via conjunction. Therefore, the answer is yes.