Consider the following premises. Elisabeth is listening to a song if and only if Jennifer is a nurse. If John were a sailor, then it is overcast. Jennifer is a nurse if and only if it is overcast. It is cold. Elisabeth is not listening to a song. Can we infer the following from them? It is cold and John is not a sailor.
 From the fact that Elisabeth is listening to a song if and only if Jennifer is a nurse, and that Elisabeth is not listening to a song we can infer that Jennifer is not a nurse. From the fact that Jennifer is a nurse if and only if it is overcast, and that Jennifer is not a nurse we can infer that it is not overcast. From the fact that if John were a sailor, then it is overcast, and that it is not overcast we can infer that John is not a sailor. Finally, from the fact that it is cold, and that John is not a sailor we can infer that it is cold and John is not a sailor. Therefore, the answer is yes.