Consider the following premises. It is sunny if and only if Richard is a doctor. It is not sunny. It is cloudy. Can we infer the following from them? Richard is not a doctor and it is cloudy.
 From the fact that it is sunny if and only if Richard is a doctor we can infer that if Richard were a doctor, then it is sunny. From the fact that if Richard were a doctor, then it is sunny, and that it is not sunny we can infer that Richard is not a doctor. Finally, from the fact that Richard is not a doctor, and that it is cloudy we can infer that Richard is not a doctor and it is cloudy. Therefore, the answer is yes.