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