Consider the following premises. If it is overcast, then it is cloudy. If it is overcast, then Charles is playing a game. If it is cloudy, then it is overcast. Charles is not playing a game. Can we infer the following from them? It is not cloudy.
 From the fact that if it is overcast, then Charles is playing a game, and that Charles is not playing a game we can infer that it is not overcast. From the fact that if it is cloudy, then it is overcast, and that if it is overcast, then it is cloudy we can infer that it is cloudy if and only if it is overcast. Finally, from the fact that it is cloudy if and only if it is overcast, and that it is not overcast we can infer that it is not cloudy. Therefore, the answer is yes.