Consider the following premises. For all x_6, x_6 will work or x_6 will not play a game. For all x_6, x_6 is a politician or x_6 will play a game. For all x_6, if x_6 were a politician, then x_6 is working. There is at least one x_6 for which x_6 is an astronaut. Can we infer the following from them? For all x_6, either x_6 will work or x_6 is an astronaut are not true.
 From the fact that for all x_6, x_6 will work or x_6 will not play a game we can infer that for all x_6, if x_6 plays a game, then x_6 is working. From the fact that for all x_6, if x_6 were a politician, then x_6 is working, that for all x_6, if x_6 plays a game, then x_6 is working, and that for all x_6, x_6 is a politician or x_6 will play a game we can infer that for all x_6, x_6 will work. Finally, from the fact that for all x_6, x_6 will work, and that there is at least one x_6 for which x_6 is an astronaut we can infer that there is at least one x_6 for which x_6 will work and x_6 is an astronaut, which contradicts that For all x_6, either x_6 will work or x_6 is an astronaut are not true. Therefore, the answer is no.