Consider the following premises. For all x_5, x_5 is not a janitor. For all x_5, x_5 is poor if and only if x_5 will play a game. For all x_5, if x_5 writes a letter, then x_5 is a janitor. For all x_5, x_5 will write a letter if and only if x_5 will play a game. Can we infer the following from them? There is at least one x_5 for which x_5 is poor.
 From the fact that for all x_5, if x_5 writes a letter, then x_5 is a janitor, and that for all x_5, x_5 is not a janitor we can infer that for all x_5, x_5 will not write a letter. From the fact that for all x_5, x_5 will write a letter if and only if x_5 will play a game, and that for all x_5, x_5 will not write a letter we can infer that for all x_5, x_5 will not play a game. Finally, from the fact that for all x_5, x_5 is poor if and only if x_5 will play a game, and that for all x_5, x_5 will not play a game we can infer that for all x_5, x_5 is not poor, which contradicts that There is at least one x_5 for which x_5 is poor. Therefore, the answer is no.