Consider the following premises. Elisabeth is cooking if and only if it is cold. It is overcast if and only if it is cold. Elisabeth is not cooking. Can we infer the following from them? It is overcast.
 From the fact that Elisabeth is cooking if and only if it is cold, and that Elisabeth is not cooking we can infer that it is not cold. Finally, from the fact that it is overcast if and only if it is cold, and that it is not cold we can infer that it is not overcast, which contradicts that It is overcast. Therefore, the answer is no.