Consider the following premises. If it is cold, then David is playing tennis. If it is overcast, then it is cold. If David plays tennis, then it is overcast. If it is cold, then it is overcast. Can we infer the following from them? If is not true that it is overcast if and only if it is cold.
 From the fact that if it is cold, then David is playing tennis, and that if David plays tennis, then it is overcast we can infer that if it is cold, then it is overcast. Finally, from the fact that if it is overcast, then it is cold, and that if it is cold, then it is overcast we can infer that it is overcast if and only if it is cold, which contradicts that If is not true that it is overcast if and only if it is cold. Therefore, the answer is no.