Consider the following premises. If John plays tennis, then Jennifer is sad. If Jennifer were sad, then it is cold. If it is cold, then Jennifer is sad. If Jennifer were sad, then John is playing tennis. It is not cold. Can we infer the following from them? John is not playing tennis.
 From the fact that if Jennifer were sad, then John is playing tennis, and that if John plays tennis, then Jennifer is sad we can infer that Jennifer is sad if and only if John is playing tennis. From the fact that if Jennifer were sad, then it is cold, and that if it is cold, then Jennifer is sad we can infer that Jennifer is sad if and only if it is cold. From the fact that Jennifer is sad if and only if it is cold, and that it is not cold we can infer that Jennifer is not sad. Finally, from the fact that Jennifer is sad if and only if John is playing tennis, and that Jennifer is not sad we can infer that John is not playing tennis. Therefore, the answer is yes.