Consider the following premises. Robert is cooking and James is a nurse. Robert is cooking if and only if Sarah is reading a book. Can we infer the following from them? Sarah is reading a book.
 From the fact that Robert is cooking if and only if Sarah is reading a book we can infer that if Robert cooks, then Sarah is reading a book. From the fact that Robert is cooking and James is a nurse we can infer that Robert is cooking. Finally, from the fact that if Robert cooks, then Sarah is reading a book, and that Robert is cooking we can infer that Sarah is reading a book. Therefore, the answer is yes.