Consider the following premises. For all x_9, x_9 is not a police officer. For all x_9, x_9 will read a book or x_9 will play a game. For all x_9, x_9 will read a book if and only if x_9 is a police officer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_2 for which x_2 will play a game.
 From the fact that for all x_9, x_9 will read a book if and only if x_9 is a police officer, and that for all x_9, x_9 is not a police officer we can infer that for all x_9, x_9 will not read a book via universal biconditional elimination. From the fact that for all x_9, x_9 will read a book or x_9 will play a game, and that for all x_9, x_9 will not read a book we can infer that for all x_9, x_9 will play a game via universal disjunctive syllogism. From the fact that for all x_9, x_9 will play a game we can infer that Mary is playing a game via universal instantiation. Finally, from the fact that Mary is playing a game we can infer that there is at least one x_2 for which x_2 will play a game via existential generalization. Therefore, the answer is yes.