Consider the following premises. Elisabeth is playing tennis if and only if it is overcast. It is not overcast. It is cold if and only if it is cloudy. If it is cloudy, then Elisabeth is playing tennis. Can we infer the following from them? It is not cold.
 From the fact that Elisabeth is playing tennis if and only if it is overcast, and that it is not overcast we can infer that Elisabeth is not playing tennis. From the fact that if it is cloudy, then Elisabeth is playing tennis, and that Elisabeth is not playing tennis we can infer that it is not cloudy. Finally, from the fact that it is cold if and only if it is cloudy, and that it is not cloudy we can infer that it is not cold. Therefore, the answer is yes.