Consider the following premises. It is overcast if and only if Jessica is reading a book. Karen is taking a plane or it is raining. Karen is taking a plane if and only if Jessica is reading a book. It is not overcast. Can we infer the following from them? It is raining.
 From the fact that it is overcast if and only if Jessica is reading a book, and that it is not overcast we can infer that Jessica is not reading a book. From the fact that Karen is taking a plane if and only if Jessica is reading a book, and that Jessica is not reading a book we can infer that Karen is not taking a plane. Finally, from the fact that Karen is taking a plane or it is raining, and that Karen is not taking a plane we can infer that it is raining. Therefore, the answer is yes.