Consider the following premises. For all x_4, if x_4 reads a book, then x_4 is cooking. For all x_4, x_4 will not read a book. For all x_4, x_4 will cook if and only if x_4 will read a book. Can we infer the following from them? For all x_4, x_4 will not cook.
 From the fact that for all x_4, x_4 will cook if and only if x_4 will read a book we can infer that for all x_4, if x_4 cooks, then x_4 is reading a book. From the fact that for all x_4, if x_4 cooks, then x_4 is reading a book, and that for all x_4, if x_4 reads a book, then x_4 is cooking we can infer that for all x_4, x_4 will cook if and only if x_4 will read a book. Finally, from the fact that for all x_4, x_4 will cook if and only if x_4 will read a book, and that for all x_4, x_4 will not read a book we can infer that for all x_4, x_4 will not cook. Therefore, the answer is yes.