Consider the following premises. For all x_9, x_9 will drink water and x_9 will cook. For all x_9, x_9 will listen to a song. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which x will listen to a song.
 From the fact that for all x_9, x_9 will drink water and x_9 will cook we can infer that for all x_9, x_9 will drink water via universal simplification. From the fact that for all x_9, x_9 will listen to a song, and that for all x_9, x_9 will drink water we can infer that for all x_9, x_9 will listen to a song and x_9 will drink water via universal conjunction. From the fact that for all x_9, x_9 will listen to a song and x_9 will drink water we can infer that for all x_9, x_9 will listen to a song via universal simplification. From the fact that for all x_9, x_9 will listen to a song we can infer that James is listening to a song via universal instantiation. Finally, from the fact that James is listening to a song we can infer that there is at least one x for which x will listen to a song via existential generalization. Therefore, the answer is yes.