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