Consider the following premises. It is cloudy if and only if it is sunny. David is not sad. Michael is playing tennis if and only if it is sunny. If it is cloudy, then David is sad. Can we infer the following from them? Michael is not playing tennis.
 From the fact that it is cloudy if and only if it is sunny we can infer that if it is sunny, then it is cloudy. From the fact that if it is sunny, then it is cloudy, and that if it is cloudy, then David is sad we can infer that if it is sunny, then David is sad. From the fact that if it is sunny, then David is sad, and that David is not sad we can infer that it is not sunny. Finally, from the fact that Michael is playing tennis if and only if it is sunny, and that it is not sunny we can infer that Michael is not playing tennis. Therefore, the answer is yes.