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