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