Consider the following premises. If Thomas cooks, then William is not excited. It is not raining. William is excited. If Robert plays a game, then it is raining. Can we infer the following from them? If we can, name the inference rule being used: Robert is not playing a game and Thomas is not cooking.
 From the fact that if Thomas cooks, then William is not excited, and that William is excited we can infer that Thomas is not cooking via modus tollens. From the fact that if Robert plays a game, then it is raining, and that it is not raining we can infer that Robert is not playing a game via modus tollens. Finally, from the fact that Robert is not playing a game, and that Thomas is not cooking we can infer that Robert is not playing a game and Thomas is not cooking via conjunction. Therefore, the answer is yes.