Consider the following premises. If Jessica were fast, then William is an office clerk. If William were an office clerk, then Jessica is fast. If William were not an office clerk, then it is cloudy. If Jessica were fast, then William is not a politician. William is a politician. Can we infer the following from them? It is not cloudy.
 From the fact that if William were an office clerk, then Jessica is fast, and that if Jessica were fast, then William is an office clerk we can infer that William is an office clerk if and only if Jessica is fast. From the fact that if Jessica were fast, then William is not a politician, and that William is a politician we can infer that Jessica is not fast. From the fact that William is an office clerk if and only if Jessica is fast, and that Jessica is not fast we can infer that William is not an office clerk. Finally, from the fact that if William were not an office clerk, then it is cloudy, and that William is not an office clerk we can infer that it is cloudy, which contradicts that It is not cloudy. Therefore, the answer is no.