Consider the following premises. For all x_8, x_8 will not play a game. For all x_8, x_8 will write a letter if and only if x_8 will work. For all x_8, x_8 will work if and only if x_8 is a police officer. For all x_8, x_8 will write a letter if and only if x_8 will play a game. Can we infer the following from them? There is at least one x_8 for which x_8 is a police officer.
 From the fact that for all x_8, x_8 will write a letter if and only if x_8 will play a game, and that for all x_8, x_8 will not play a game we can infer that for all x_8, x_8 will not write a letter. From the fact that for all x_8, x_8 will write a letter if and only if x_8 will work, and that for all x_8, x_8 will not write a letter we can infer that for all x_8, x_8 will not work. Finally, from the fact that for all x_8, x_8 will work if and only if x_8 is a police officer, and that for all x_8, x_8 will not work we can infer that for all x_8, x_8 is not a police officer, which contradicts that There is at least one x_8 for which x_8 is a police officer. Therefore, the answer is no.