Consider the following premises. If Karen were a sailor, then it is cloudy. If Charles plays a game, then Karen is a sailor. It is cloudy if and only if Charles is playing a game. Can we infer the following from them? It is cloudy if and only if Karen is a sailor.
 From the fact that it is cloudy if and only if Charles is playing a game we can infer that if it is cloudy, then Charles is playing a game. From the fact that if it is cloudy, then Charles is playing a game, and that if Charles plays a game, then Karen is a sailor we can infer that if it is cloudy, then Karen is a sailor. Finally, from the fact that if it is cloudy, then Karen is a sailor, and that if Karen were a sailor, then it is cloudy we can infer that it is cloudy if and only if Karen is a sailor. Therefore, the answer is yes.