Consider the following premises. Patricia is not working. If Patricia works, then it is raining. Patricia is a doctor if and only if it is raining. If it rains, then Patricia is working. Can we infer the following from them? Patricia is not a doctor.
 From the fact that if Patricia works, then it is raining, and that if it rains, then Patricia is working we can infer that Patricia is working if and only if it is raining. From the fact that Patricia is working if and only if it is raining, and that Patricia is not working we can infer that it is not raining. Finally, from the fact that Patricia is a doctor if and only if it is raining, and that it is not raining we can infer that Patricia is not a doctor. Therefore, the answer is yes.