Consider the following premises. For all y, if y plays tennis, then y is playing a game. For all y, y is not a writer. For all y, if y plays a game, then y is playing tennis. For all y, y is a writer if and only if y will drive a car. There is at least one y for which y will drive a car if and only if y will play a game. Can we infer the following from them? There is at least one y for which y will not play tennis.
 From the fact that for all y, y is a writer if and only if y will drive a car, and that for all y, y is not a writer we can infer that for all y, y will not drive a car. From the fact that there is at least one y for which y will drive a car if and only if y will play a game, and that for all y, y will not drive a car we can infer that there is at least one y for which y will not play a game. From the fact that for all y, if y plays tennis, then y is playing a game, and that for all y, if y plays a game, then y is playing tennis we can infer that for all y, y will play tennis if and only if y will play a game. Finally, from the fact that for all y, y will play tennis if and only if y will play a game, and that there is at least one y for which y will not play a game we can infer that there is at least one y for which y will not play tennis. Therefore, the answer is yes.