Consider the following premises. If William cooks, then David is reading a book. It is not late. It is late or Joseph is running. If David reads a book, then Joseph is not running. Can we infer the following from them? William is not cooking.
 From the fact that it is late or Joseph is running, and that it is not late we can infer that Joseph is running. From the fact that if David reads a book, then Joseph is not running, and that Joseph is running we can infer that David is not reading a book. Finally, from the fact that if William cooks, then David is reading a book, and that David is not reading a book we can infer that William is not cooking. Therefore, the answer is yes.