Consider the following premises. For all x_11, if x_11 plays a game, then x_11 is playing tennis. For all x_11, x_11 will play tennis if and only if x_11 will play a game. Sarah is not playing tennis. Can we infer the following from them? Sarah is not playing a game.
 From the fact that for all x_11, x_11 will play tennis if and only if x_11 will play a game we can infer that for all x_11, if x_11 plays tennis, then x_11 is playing a game. From the fact that for all x_11, if x_11 plays tennis, then x_11 is playing a game, and that for all x_11, if x_11 plays a game, then x_11 is playing tennis we can infer that for all x_11, x_11 will play tennis if and only if x_11 will play a game. From the fact that for all x_11, x_11 will play tennis if and only if x_11 will play a game we can infer that Sarah is playing tennis if and only if Sarah is playing a game. From the fact that Sarah is playing tennis if and only if Sarah is playing a game we can infer that if Sarah plays a game, then Sarah is playing tennis. Finally, from the fact that if Sarah plays a game, then Sarah is playing tennis, and that Sarah is not playing tennis we can infer that Sarah is not playing a game. Therefore, the answer is yes.