Consider the following premises. Jessica is climbing a mountain if and only if Jessica is playing tennis. For all z_2, if z_2 plays tennis, then z_2 is climbing a mountain. Can we infer the following from them? Jessica is playing tennis if and only if Jessica is climbing a mountain.
 From the fact that for all z_2, if z_2 plays tennis, then z_2 is climbing a mountain we can infer that if Jessica plays tennis, then Jessica is climbing a mountain. From the fact that Jessica is climbing a mountain if and only if Jessica is playing tennis we can infer that if Jessica climbs a mountain, then Jessica is playing tennis. Finally, from the fact that if Jessica plays tennis, then Jessica is climbing a mountain, and that if Jessica climbs a mountain, then Jessica is playing tennis we can infer that Jessica is playing tennis if and only if Jessica is climbing a mountain. Therefore, the answer is yes.