Consider the following premises. There is at least one y for which y will not drink water. For all y, if y drinks water, then y is listening to a song. For all y, if y listens to a song, then y is drinking water. For all y, y will listen to a song if and only if y is an astronaut. Can we infer the following from them? For all y, y is an astronaut.
 From the fact that for all y, if y drinks water, then y is listening to a song, and that for all y, if y listens to a song, then y is drinking water we can infer that for all y, y will drink water if and only if y will listen to a song. From the fact that for all y, y will drink water if and only if y will listen to a song, and that there is at least one y for which y will not drink water we can infer that there is at least one y for which y will not listen to a song. Finally, from the fact that for all y, y will listen to a song if and only if y is an astronaut, and that there is at least one y for which y will not listen to a song we can infer that there is at least one y for which y is not an astronaut, which contradicts that For all y, y is an astronaut. Therefore, the answer is no.