Consider the following premises. There is at least one x_4 for which if x_4 reads a book, then x_4 is writing a letter. For all x_4, x_4 will read a book or x_4 will not write a letter. Can we infer the following from them? There is at least one x_4 for which if x_4 writes a letter, then x_4 is reading a book.
 From the fact that for all x_4, x_4 will read a book or x_4 will not write a letter we can infer that for all x_4, if x_4 writes a letter, then x_4 is reading a book. From the fact that for all x_4, if x_4 writes a letter, then x_4 is reading a book, and that there is at least one x_4 for which if x_4 reads a book, then x_4 is writing a letter we can infer that there is at least one x_4 for which x_4 will write a letter if and only if x_4 will read a book. Finally, from the fact that there is at least one x_4 for which x_4 will write a letter if and only if x_4 will read a book we can infer that there is at least one x_4 for which if x_4 writes a letter, then x_4 is reading a book. Therefore, the answer is yes.