Consider the following premises. For all x_2, if x_2 listens to a song, then x_2 is not driving a car. For all x_2, if x_2 were a writer, then x_2 is listening to a song. For all x_2, x_2 will drive a car. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, x_2 is not a writer.
 From the fact that for all x_2, if x_2 listens to a song, then x_2 is not driving a car, and that for all x_2, x_2 will drive a car we can infer that for all x_2, x_2 will not listen to a song via universal modus tollens. Finally, from the fact that for all x_2, if x_2 were a writer, then x_2 is listening to a song, and that for all x_2, x_2 will not listen to a song we can infer that for all x_2, x_2 is not a writer via universal modus tollens. Therefore, the answer is yes.