Consider the following premises. There is at least one x_3 for which x_3 will play a game or x_3 is not poor. For all x_3, x_3 is poor. Can we infer the following from them? For all x_3, x_3 will not play a game.
 From the fact that there is at least one x_3 for which x_3 will play a game or x_3 is not poor we can infer that there is at least one x_3 for which if x_3 were poor, then x_3 is playing a game. Finally, from the fact that there is at least one x_3 for which if x_3 were poor, then x_3 is playing a game, and that for all x_3, x_3 is poor we can infer that there is at least one x_3 for which x_3 will play a game, which contradicts that For all x_3, x_3 will not play a game. Therefore, the answer is no.