Consider the following premises. If it is late, then it is cloudy. If it is cloudy, then William is fast. It is late if and only if William is fast. Can we infer the following from them? William is fast if and only if it is late.
 From the fact that it is late if and only if William is fast we can infer that if William were fast, then it is late. From the fact that if it is late, then it is cloudy, and that if it is cloudy, then William is fast we can infer that if it is late, then William is fast. Finally, from the fact that if William were fast, then it is late, and that if it is late, then William is fast we can infer that William is fast if and only if it is late. Therefore, the answer is yes.