Consider the following premises. For all y, y will play a game or y will not listen to a song. For all y, y will listen to a song. There is at least one y for which if y reads a book, then y is playing a game. Can we infer the following from them? For all y, y will not play a game.
 From the fact that for all y, y will play a game or y will not listen to a song we can infer that for all y, if y listens to a song, then y is playing a game. From the fact that for all y, y will listen to a song we can infer that for all y, y will listen to a song or y will read a book. Finally, from the fact that for all y, if y listens to a song, then y is playing a game, that there is at least one y for which if y reads a book, then y is playing a game, and that for all y, y will listen to a song or y will read a book we can infer that there is at least one y for which y will play a game, which contradicts that For all y, y will not play a game. Therefore, the answer is no.