Consider the following premises. It is cloudy if and only if Thomas is a doctor. If Karen were an astronaut, then Thomas is a doctor. If it is cloudy, then Karen is an astronaut. Can we infer the following from them? If it is cloudy, then Thomas is a doctor.
 From the fact that it is cloudy if and only if Thomas is a doctor we can infer that if Thomas were a doctor, then it is cloudy. Finally, from the fact that if it is cloudy, then Karen is an astronaut, and that if Karen were an astronaut, then Thomas is a doctor we can infer that if it is cloudy, then Thomas is a doctor. Therefore, the answer is yes.