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