Consider the following premises. For all y_4, y_4 will play tennis. Joseph is bored. For all y_4, if y_4 plays tennis, then y_4 is writing a letter. Can we infer the following from them? There is at least one y_4 for which y_4 will write a letter and y_4 is bored.
 From the fact that for all y_4, if y_4 plays tennis, then y_4 is writing a letter, and that for all y_4, y_4 will play tennis we can infer that for all y_4, y_4 will write a letter. From the fact that Joseph is bored we can infer that there is at least one y_4 for which y_4 is bored. Finally, from the fact that for all y_4, y_4 will write a letter, and that there is at least one y_4 for which y_4 is bored we can infer that there is at least one y_4 for which y_4 will write a letter and y_4 is bored. Therefore, the answer is yes.