Consider the following premises. For all z_3, z_3 is a carpenter if and only if z_3 is sad. For all z_3, z_3 is a carpenter or z_3 will not listen to a song. Can we infer the following from them? There is at least one z_3 for which the fact that z_3 listens to a song does not imply that z_3 is sad.
 From the fact that for all z_3, z_3 is a carpenter if and only if z_3 is sad we can infer that for all z_3, if z_3 were a carpenter, then z_3 is sad. From the fact that for all z_3, z_3 is a carpenter or z_3 will not listen to a song we can infer that for all z_3, if z_3 listens to a song, then z_3 is a carpenter. Finally, from the fact that for all z_3, if z_3 listens to a song, then z_3 is a carpenter, and that for all z_3, if z_3 were a carpenter, then z_3 is sad we can infer that for all z_3, if z_3 listens to a song, then z_3 is sad, which contradicts that There is at least one z_3 for which the fact that z_3 listens to a song does not imply that z_3 is sad. Therefore, the answer is no.