Consider the following premises. If it is late, then William is cooking. If James were poor, then Karen is reading a book. If William cooks, then James is poor. If James were poor, then William is cooking. Can we infer the following from them? The fact that it is late does not imply that Karen is reading a book.
 From the fact that if William cooks, then James is poor, and that if James were poor, then William is cooking we can infer that William is cooking if and only if James is poor. From the fact that William is cooking if and only if James is poor we can infer that if William cooks, then James is poor. From the fact that if William cooks, then James is poor, and that if James were poor, then Karen is reading a book we can infer that if William cooks, then Karen is reading a book. Finally, from the fact that if it is late, then William is cooking, and that if William cooks, then Karen is reading a book we can infer that if it is late, then Karen is reading a book, which contradicts that The fact that it is late does not imply that Karen is reading a book. Therefore, the answer is no.