Consider the following premises. For all x_2, x_2 will play tennis if and only if x_2 is sad. Charles is not a carpenter. If Sarah climbs a mountain, then Charles is a carpenter. Karen is sad if and only if Sarah is climbing a mountain. Can we infer the following from them? Karen is playing tennis.
 From the fact that for all x_2, x_2 will play tennis if and only if x_2 is sad we can infer that Karen is playing tennis if and only if Karen is sad. From the fact that if Sarah climbs a mountain, then Charles is a carpenter, and that Charles is not a carpenter we can infer that Sarah is not climbing a mountain. From the fact that Karen is sad if and only if Sarah is climbing a mountain, and that Sarah is not climbing a mountain we can infer that Karen is not sad. Finally, from the fact that Karen is playing tennis if and only if Karen is sad, and that Karen is not sad we can infer that Karen is not playing tennis, which contradicts that Karen is playing tennis. Therefore, the answer is no.