Consider the following premises. If Richard were a nurse, then William is a janitor. If Richard were not a nurse, then it is overcast. William is a janitor if and only if Michael is reading a book. Michael is not reading a book. Can we infer the following from them? If we can, name the inference rule being used: It is overcast.
 From the fact that William is a janitor if and only if Michael is reading a book, and that Michael is not reading a book we can infer that William is not a janitor via biconditional elimination. From the fact that if Richard were a nurse, then William is a janitor, and that William is not a janitor we can infer that Richard is not a nurse via modus tollens. Finally, from the fact that if Richard were not a nurse, then it is overcast, and that Richard is not a nurse we can infer that it is overcast via modus ponens. Therefore, the answer is yes.