Consider the following premises. For all z_3, z_3 will sleep if and only if z_3 will cook. Charles is not sleeping. Barbara is listening to a song if and only if Charles is cooking. Can we infer the following from them? Barbara is not listening to a song.
 From the fact that for all z_3, z_3 will sleep if and only if z_3 will cook we can infer that Charles is sleeping if and only if Charles is cooking. From the fact that Charles is sleeping if and only if Charles is cooking, and that Charles is not sleeping we can infer that Charles is not cooking. Finally, from the fact that Barbara is listening to a song if and only if Charles is cooking, and that Charles is not cooking we can infer that Barbara is not listening to a song. Therefore, the answer is yes.