Consider the following premises. William is sad if and only if James is playing a game. It is windy if and only if Mary is listening to a song. It is windy if and only if William is sad. Elisabeth is running if and only if James is playing a game. Elisabeth is not running. Can we infer the following from them? Mary is not listening to a song.
 From the fact that Elisabeth is running if and only if James is playing a game, and that Elisabeth is not running we can infer that James is not playing a game. From the fact that William is sad if and only if James is playing a game, and that James is not playing a game we can infer that William is not sad. From the fact that it is windy if and only if William is sad, and that William is not sad we can infer that it is not windy. Finally, from the fact that it is windy if and only if Mary is listening to a song, and that it is not windy we can infer that Mary is not listening to a song. Therefore, the answer is yes.