Consider the following premises. Joseph is a nurse or Sarah is sleeping. Patricia is a soldier. If Sarah sleeps, then Patricia is not a soldier. Can we infer the following from them? Joseph is a nurse.
 From the fact that if Sarah sleeps, then Patricia is not a soldier, and that Patricia is a soldier we can infer that Sarah is not sleeping. From the fact that Joseph is a nurse or Sarah is sleeping we can infer that if Sarah doesn't sleep, then Joseph is a nurse. Finally, from the fact that if Sarah doesn't sleep, then Joseph is a nurse, and that Sarah is not sleeping we can infer that Joseph is a nurse. Therefore, the answer is yes.