Consider the following premises. For all x_8, x_8 will play a game or x_8 will listen to a song. For all x_8, x_8 will not play a game. For all x_8, if x_8 listens to a song, then x_8 is a police officer. For all x_8, x_8 will work. For all x_8, if x_8 writes a letter, then x_8 is a police officer. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will work.
That is one of the premises. Therefore, the answer is yes.