Consider the following premises. For all x_2, x_2 will not drink water. For all x_2, x_2 will play tennis if and only if x_2 will drink water. For all x_2, x_2 will play tennis or x_2 will not drink water. Can we infer the following from them? For all x_2, x_2 will not play tennis.
 From the fact that for all x_2, x_2 will play tennis or x_2 will not drink water we can infer that for all x_2, if x_2 drinks water, then x_2 is playing tennis. From the fact that for all x_2, x_2 will play tennis if and only if x_2 will drink water we can infer that for all x_2, if x_2 plays tennis, then x_2 is drinking water. From the fact that for all x_2, if x_2 drinks water, then x_2 is playing tennis, and that for all x_2, if x_2 plays tennis, then x_2 is drinking water we can infer that for all x_2, x_2 will drink water if and only if x_2 will play tennis. Finally, from the fact that for all x_2, x_2 will drink water if and only if x_2 will play tennis, and that for all x_2, x_2 will not drink water we can infer that for all x_2, x_2 will not play tennis. Therefore, the answer is yes.