Consider the following premises. For all z_2, if z_2 plays tennis, then z_2 is drinking water. Mary is not drinking water. For all z_2, z_2 will drink water if and only if z_2 will play tennis. Can we infer the following from them? If we can, name the inference rule being used: Mary is playing tennis.
 From the fact that for all z_2, z_2 will drink water if and only if z_2 will play tennis we can infer that for all z_2, if z_2 drinks water, then z_2 is playing tennis via universal biconditional elimination. From the fact that for all z_2, if z_2 drinks water, then z_2 is playing tennis, and that for all z_2, if z_2 plays tennis, then z_2 is drinking water we can infer that for all z_2, z_2 will drink water if and only if z_2 will play tennis via universal biconditional introduction. From the fact that for all z_2, z_2 will drink water if and only if z_2 will play tennis we can infer that Mary is drinking water if and only if Mary is playing tennis via universal instantiation. From the fact that Mary is drinking water if and only if Mary is playing tennis we can infer that if Mary plays tennis, then Mary is drinking water via biconditional elimination. Finally, from the fact that if Mary plays tennis, then Mary is drinking water, and that Mary is not drinking water we can infer that Mary is not playing tennis via modus tollens, which contradicts that Mary is playing tennis. Therefore, the answer is no.