Consider the following premises. It is late if and only if William is reading a book. If it is windy, then it is late. If Joseph listens to a song, then it is windy. Can we infer the following from them? If Joseph listens to a song, then William is reading a book.
 From the fact that if Joseph listens to a song, then it is windy, and that if it is windy, then it is late we can infer that if Joseph listens to a song, then it is late. From the fact that it is late if and only if William is reading a book we can infer that if it is late, then William is reading a book. Finally, from the fact that if Joseph listens to a song, then it is late, and that if it is late, then William is reading a book we can infer that if Joseph listens to a song, then William is reading a book. Therefore, the answer is yes.