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