Consider the following premises. It is cloudy if and only if Charles is a doctor. If it is cloudy, then Sarah is playing squash. Sarah is not playing squash. If Richard were a carpenter, then Charles is a doctor. Can we infer the following from them? If we can, name the inference rule being used: Richard is not a carpenter.
 From the fact that it is cloudy if and only if Charles is a doctor we can infer that if Charles were a doctor, then it is cloudy via biconditional elimination. From the fact that if it is cloudy, then Sarah is playing squash, and that Sarah is not playing squash we can infer that it is not cloudy via modus tollens. From the fact that if Charles were a doctor, then it is cloudy, and that it is not cloudy we can infer that Charles is not a doctor via modus tollens. Finally, from the fact that if Richard were a carpenter, then Charles is a doctor, and that Charles is not a doctor we can infer that Richard is not a carpenter via modus tollens. Therefore, the answer is yes.