Consider the following premises. For all z_3, z_3 will listen to a song or z_3 will not drive a car. For all z_3, if z_3 listens to a song, then z_3 is driving a car. Can we infer the following from them? For all z_3, z_3 will drive a car if and only if z_3 will listen to a song.
 From the fact that for all z_3, z_3 will listen to a song or z_3 will not drive a car we can infer that for all z_3, if z_3 drives a car, then z_3 is listening to a song. Finally, from the fact that for all z_3, if z_3 drives a car, then z_3 is listening to a song, and that for all z_3, if z_3 listens to a song, then z_3 is driving a car we can infer that for all z_3, z_3 will drive a car if and only if z_3 will listen to a song. Therefore, the answer is yes.