Consider the following premises. It is late if and only if Richard is playing a game. Richard is not playing a game. If it is late, then Richard is playing a game. Can we infer the following from them? It is not late or James is rich.
 From the fact that it is late if and only if Richard is playing a game we can infer that if Richard plays a game, then it is late. From the fact that if Richard plays a game, then it is late, and that if it is late, then Richard is playing a game we can infer that Richard is playing a game if and only if it is late. From the fact that Richard is playing a game if and only if it is late, and that Richard is not playing a game we can infer that it is not late. Finally, from the fact that it is not late we can infer that it is not late or James is rich. Therefore, the answer is yes.