Consider the following premises. James is a politician if and only if Barbara is working. For all x, x is not a politician. For all x_12, x_12 will listen to a song if and only if x_12 will work. Can we infer the following from them? Barbara is not listening to a song.
 From the fact that for all x_12, x_12 will listen to a song if and only if x_12 will work we can infer that Barbara is listening to a song if and only if Barbara is working. From the fact that for all x, x is not a politician we can infer that James is not a politician. From the fact that James is a politician if and only if Barbara is working, and that James is not a politician we can infer that Barbara is not working. Finally, from the fact that Barbara is listening to a song if and only if Barbara is working, and that Barbara is not working we can infer that Barbara is not listening to a song. Therefore, the answer is yes.