Consider the following premises. For all x_7, x_7 is a police officer or x_7 will not listen to a song. If Barbara were a police officer, then Barbara is listening to a song. Can we infer the following from them? If is not true that Barbara is a police officer if and only if Barbara is listening to a song.
 From the fact that for all x_7, x_7 is a police officer or x_7 will not listen to a song we can infer that for all x_7, if x_7 listens to a song, then x_7 is a police officer. From the fact that for all x_7, if x_7 listens to a song, then x_7 is a police officer we can infer that if Barbara listens to a song, then Barbara is a police officer. Finally, from the fact that if Barbara were a police officer, then Barbara is listening to a song, and that if Barbara listens to a song, then Barbara is a police officer we can infer that Barbara is a police officer if and only if Barbara is listening to a song, which contradicts that If is not true that Barbara is a police officer if and only if Barbara is listening to a song. Therefore, the answer is no.