Consider the following premises. If it is cloudy, then Elisabeth is an astronaut. David is a server if and only if it is snowing. If Elisabeth were an astronaut, then it is snowing. David is not a server. Can we infer the following from them? It is cloudy.
 From the fact that if it is cloudy, then Elisabeth is an astronaut, and that if Elisabeth were an astronaut, then it is snowing we can infer that if it is cloudy, then it is snowing. From the fact that David is a server if and only if it is snowing, and that David is not a server we can infer that it is not snowing. Finally, from the fact that if it is cloudy, then it is snowing, and that it is not snowing we can infer that it is not cloudy, which contradicts that It is cloudy. Therefore, the answer is no.