Consider the following premises. For all x_12, if x_12 were a police officer, then x_12 is an artist. For all x_12, x_12 will not play tennis. For all x_12, if x_12 were a nurse, then x_12 is a police officer. For all x_12, x_12 will play tennis if and only if x_12 is an artist. Can we infer the following from them? For all x_12, x_12 is not a nurse.
 From the fact that for all x_12, x_12 will play tennis if and only if x_12 is an artist we can infer that for all x_12, if x_12 were an artist, then x_12 is playing tennis. From the fact that for all x_12, if x_12 were a police officer, then x_12 is an artist, and that for all x_12, if x_12 were an artist, then x_12 is playing tennis we can infer that for all x_12, if x_12 were a police officer, then x_12 is playing tennis. From the fact that for all x_12, if x_12 were a nurse, then x_12 is a police officer, and that for all x_12, if x_12 were a police officer, then x_12 is playing tennis we can infer that for all x_12, if x_12 were a nurse, then x_12 is playing tennis. Finally, from the fact that for all x_12, if x_12 were a nurse, then x_12 is playing tennis, and that for all x_12, x_12 will not play tennis we can infer that for all x_12, x_12 is not a nurse. Therefore, the answer is yes.