Consider the following premises. For all z, if z were a carpenter, then z is listening to a song. For all z, z will listen to a song if and only if z is a carpenter. For all z, if z were a carpenter, then z is not a sailor. For all z, z is a sailor. Can we infer the following from them? For all z, z will not listen to a song.
 From the fact that for all z, if z were a carpenter, then z is not a sailor, and that for all z, z is a sailor we can infer that for all z, z is not a carpenter. From the fact that for all z, z will listen to a song if and only if z is a carpenter we can infer that for all z, if z listens to a song, then z is a carpenter. From the fact that for all z, if z were a carpenter, then z is listening to a song, and that for all z, if z listens to a song, then z is a carpenter we can infer that for all z, z is a carpenter if and only if z will listen to a song. Finally, from the fact that for all z, z is a carpenter if and only if z will listen to a song, and that for all z, z is not a carpenter we can infer that for all z, z will not listen to a song. Therefore, the answer is yes.