Consider the following premises. For all x_1, x_1 will play a game. For all x_1, if x_1 plays a game, then x_1 is a carpenter. For all x_1, x_1 will play tennis. Can we infer the following from them? If we can, name the inference rule being used: For all x_1, x_1 will play tennis and x_1 is a carpenter.
 From the fact that for all x_1, if x_1 plays a game, then x_1 is a carpenter, and that for all x_1, x_1 will play a game we can infer that for all x_1, x_1 is a carpenter via universal modus ponens. Finally, from the fact that for all x_1, x_1 will play tennis, and that for all x_1, x_1 is a carpenter we can infer that for all x_1, x_1 will play tennis and x_1 is a carpenter via universal conjunction. Therefore, the answer is yes.