Consider the following premises. For all x_8, x_8 will read a book. There is at least one x_8 for which x_8 will play squash and x_8 will play tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 will read a book.
 From the fact that there is at least one x_8 for which x_8 will play squash and x_8 will play tennis we can infer that there is at least one x_8 for which x_8 will play squash via existential simplification. From the fact that there is at least one x_8 for which x_8 will play squash, and that for all x_8, x_8 will read a book we can infer that there is at least one x_8 for which x_8 will play squash and x_8 will read a book via existential conjunction. Finally, from the fact that there is at least one x_8 for which x_8 will play squash and x_8 will read a book we can infer that there is at least one x_8 for which x_8 will read a book via existential simplification. Therefore, the answer is yes.