Consider the following premises. Barbara is driving a car if and only if Jessica is sleeping. Jennifer is not writing a letter. If Barbara drives a car, then Jennifer is writing a letter. Can we infer the following from them? Jessica is not sleeping or it is cloudy.
 From the fact that if Barbara drives a car, then Jennifer is writing a letter, and that Jennifer is not writing a letter we can infer that Barbara is not driving a car. From the fact that Barbara is driving a car if and only if Jessica is sleeping, and that Barbara is not driving a car we can infer that Jessica is not sleeping. Finally, from the fact that Jessica is not sleeping we can infer that Jessica is not sleeping or it is cloudy. Therefore, the answer is yes.