Consider the following premises. It is not raining. It is cloudy and Elisabeth is excited. If Elisabeth plays squash, then it is raining. If Richard listens to a song, then Elisabeth is playing squash. Can we infer the following from them? If we can, name the inference rule being used: Richard is not listening to a song and it is cloudy.
 From the fact that if Elisabeth plays squash, then it is raining, and that it is not raining we can infer that Elisabeth is not playing squash via modus tollens. From the fact that if Richard listens to a song, then Elisabeth is playing squash, and that Elisabeth is not playing squash we can infer that Richard is not listening to a song via modus tollens. From the fact that it is cloudy and Elisabeth is excited we can infer that it is cloudy via simplification. Finally, from the fact that Richard is not listening to a song, and that it is cloudy we can infer that Richard is not listening to a song and it is cloudy via conjunction. Therefore, the answer is yes.