Consider the following premises. If Jessica sleeps, then it is not overcast. Linda is not a doctor. It is raining or Linda is a doctor. It is not raining or it is overcast. Jessica is sleeping if and only if David is a poet. Can we infer the following from them? David is a poet.
 From the fact that it is raining or Linda is a doctor, and that it is not raining or it is overcast we can infer that Linda is a doctor or it is overcast. From the fact that Linda is a doctor or it is overcast, and that Linda is not a doctor we can infer that it is overcast. From the fact that if Jessica sleeps, then it is not overcast, and that it is overcast we can infer that Jessica is not sleeping. Finally, from the fact that Jessica is sleeping if and only if David is a poet, and that Jessica is not sleeping we can infer that David is not a poet, which contradicts that David is a poet. Therefore, the answer is no.