Consider the following premises. For all x_10, x_10 will listen to a song. There is at least one x_10 for which x_10 will play a game and x_10 will climb a mountain. For all x_10, if x_10 listens to a song, then x_10 is reading a book. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 will read a book and x_10 will play a game.
 From the fact that for all x_10, if x_10 listens to a song, then x_10 is reading a book, and that for all x_10, x_10 will listen to a song we can infer that for all x_10, x_10 will read a book via universal modus ponens. From the fact that there is at least one x_10 for which x_10 will play a game and x_10 will climb a mountain we can infer that there is at least one x_10 for which x_10 will play a game via existential simplification. Finally, from the fact that for all x_10, x_10 will read a book, and that there is at least one x_10 for which x_10 will play a game we can infer that there is at least one x_10 for which x_10 will read a book and x_10 will play a game via existential conjunction. Therefore, the answer is yes.