Consider the following premises. Jessica is sleeping if and only if David is driving a car. If David drives a car, then Thomas is climbing a mountain. Jessica is sleeping or Thomas is not climbing a mountain. Can we infer the following from them? Jessica is sleeping if and only if Thomas is climbing a mountain.
 From the fact that Jessica is sleeping or Thomas is not climbing a mountain we can infer that if Thomas climbs a mountain, then Jessica is sleeping. From the fact that Jessica is sleeping if and only if David is driving a car we can infer that if Jessica sleeps, then David is driving a car. From the fact that if Jessica sleeps, then David is driving a car, and that if David drives a car, then Thomas is climbing a mountain we can infer that if Jessica sleeps, then Thomas is climbing a mountain. Finally, from the fact that if Jessica sleeps, then Thomas is climbing a mountain, and that if Thomas climbs a mountain, then Jessica is sleeping we can infer that Jessica is sleeping if and only if Thomas is climbing a mountain. Therefore, the answer is yes.