Consider the following premises. For all z_4, z_4 will sleep or z_4 will not write a letter. For all z_4, z_4 will write a letter or z_4 will play tennis. For all z_4, z_4 will sleep or z_4 will not play tennis. Can we infer the following from them? For all z_4, z_4 will sleep.
 From the fact that for all z_4, z_4 will sleep or z_4 will not play tennis we can infer that for all z_4, if z_4 plays tennis, then z_4 is sleeping. From the fact that for all z_4, z_4 will sleep or z_4 will not write a letter we can infer that for all z_4, if z_4 writes a letter, then z_4 is sleeping. Finally, from the fact that for all z_4, if z_4 writes a letter, then z_4 is sleeping, that for all z_4, if z_4 plays tennis, then z_4 is sleeping, and that for all z_4, z_4 will write a letter or z_4 will play tennis we can infer that for all z_4, z_4 will sleep. Therefore, the answer is yes.