Consider the following premises. For all x_4, x_4 will not play tennis. For all x_5, if x_5 plays a game, then x_5 is a mechanic. For all x_4, x_4 will play tennis or x_4 will play a game. Can we infer the following from them? If we can, name the inference rule being used: Charles is a mechanic.
 From the fact that for all x_4, x_4 will play tennis or x_4 will play a game, and that for all x_4, x_4 will not play tennis we can infer that for all x_4, x_4 will play a game via universal disjunctive syllogism. From the fact that for all x_4, x_4 will play a game we can infer that Charles is playing a game via universal instantiation. From the fact that for all x_5, if x_5 plays a game, then x_5 is a mechanic we can infer that if Charles plays a game, then Charles is a mechanic via universal instantiation. Finally, from the fact that if Charles plays a game, then Charles is a mechanic, and that Charles is playing a game we can infer that Charles is a mechanic via modus ponens. Therefore, the answer is yes.