Consider the following premises. Jennifer is not playing a game. It is cloudy if and only if it is overcast. Thomas is sleeping. If it is cloudy, then Jennifer is playing a game. Can we infer the following from them? It is overcast.
 From the fact that if it is cloudy, then Jennifer is playing a game, and that Jennifer is not playing a game we can infer that it is not cloudy. Finally, from the fact that it is cloudy if and only if it is overcast, and that it is not cloudy we can infer that it is not overcast, which contradicts that It is overcast. Therefore, the answer is no.