Consider the following premises. If Mary climbs a mountain, then Jessica is sad. If it snows, then Jessica is sad. It is sunny if and only if Jessica is sad. If it is cloudy, then it is snowing. Mary is climbing a mountain or it is cloudy. Can we infer the following from them? It is sunny.
 From the fact that if it is cloudy, then it is snowing, and that if it snows, then Jessica is sad we can infer that if it is cloudy, then Jessica is sad. From the fact that if Mary climbs a mountain, then Jessica is sad, that if it is cloudy, then Jessica is sad, and that Mary is climbing a mountain or it is cloudy we can infer that Jessica is sad. From the fact that it is sunny if and only if Jessica is sad we can infer that if Jessica were sad, then it is sunny. Finally, from the fact that if Jessica were sad, then it is sunny, and that Jessica is sad we can infer that it is sunny. Therefore, the answer is yes.