Consider the following premises. If Mary cooks, then it is cloudy. If it is cloudy, then it is windy. Thomas is working if and only if it is windy. Can we infer the following from them? The fact that Mary cooks does not imply that Thomas is working.
 From the fact that if Mary cooks, then it is cloudy, and that if it is cloudy, then it is windy we can infer that if Mary cooks, then it is windy. From the fact that Thomas is working if and only if it is windy we can infer that if it is windy, then Thomas is working. Finally, from the fact that if Mary cooks, then it is windy, and that if it is windy, then Thomas is working we can infer that if Mary cooks, then Thomas is working, which contradicts that The fact that Mary cooks does not imply that Thomas is working. Therefore, the answer is no.