Consider the following premises. It is cloudy if and only if Barbara is cooking. Thomas is a server or it is not cloudy. Can we infer the following from them? The fact that Barbara cooks does not imply that Thomas is a server.
 From the fact that it is cloudy if and only if Barbara is cooking we can infer that if Barbara cooks, then it is cloudy. From the fact that Thomas is a server or it is not cloudy we can infer that if it is cloudy, then Thomas is a server. Finally, from the fact that if Barbara cooks, then it is cloudy, and that if it is cloudy, then Thomas is a server we can infer that if Barbara cooks, then Thomas is a server, which contradicts that The fact that Barbara cooks does not imply that Thomas is a server. Therefore, the answer is no.