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