Consider the following premises. For all x_15, x_15 will write a letter if and only if x_15 will play tennis. For all x_15, x_15 will read a book. There is at least one x_15 for which x_15 will play tennis. Can we infer the following from them? There is at least one x_15 for which x_15 will write a letter.
 From the fact that for all x_15, x_15 will write a letter if and only if x_15 will play tennis we can infer that for all x_15, if x_15 plays tennis, then x_15 is writing a letter. Finally, from the fact that for all x_15, if x_15 plays tennis, then x_15 is writing a letter, and that there is at least one x_15 for which x_15 will play tennis we can infer that there is at least one x_15 for which x_15 will write a letter. Therefore, the answer is yes.