Consider the following premises. For all x_7, x_7 will write a letter or x_7 is rich. For all x_7, x_7 will read a book. For all x_7, if x_7 writes a letter, then x_7 is not reading a book. Can we infer the following from them? There is at least one x for which x is rich.
 From the fact that for all x_7, if x_7 writes a letter, then x_7 is not reading a book, and that for all x_7, x_7 will read a book we can infer that for all x_7, x_7 will not write a letter. From the fact that for all x_7, x_7 will write a letter or x_7 is rich, and that for all x_7, x_7 will not write a letter we can infer that for all x_7, x_7 is rich. From the fact that for all x_7, x_7 is rich we can infer that Sarah is rich. Finally, from the fact that Sarah is rich we can infer that there is at least one x for which x is rich. Therefore, the answer is yes.