Consider the following premises. Michael is listening to a song or William is poor. Elisabeth is playing a game if and only if Barbara is rich. Michael is not listening to a song or Barbara is rich. If William were poor, then Elisabeth is playing a game. Can we infer the following from them? Elisabeth is playing a game.
 From the fact that Michael is listening to a song or William is poor, and that Michael is not listening to a song or Barbara is rich we can infer that William is poor or Barbara is rich. From the fact that Elisabeth is playing a game if and only if Barbara is rich we can infer that if Barbara were rich, then Elisabeth is playing a game. Finally, from the fact that if William were poor, then Elisabeth is playing a game, that if Barbara were rich, then Elisabeth is playing a game, and that William is poor or Barbara is rich we can infer that Elisabeth is playing a game. Therefore, the answer is yes.