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