Consider the following premises. Charles is a musician. If Barbara listens to a song, then Joseph is not a mechanic. Joseph is a mechanic if and only if Charles is a musician. Can we infer the following from them? If we can, name the inference rule being used: Barbara is listening to a song.
 From the fact that Joseph is a mechanic if and only if Charles is a musician we can infer that if Charles were a musician, then Joseph is a mechanic via biconditional elimination. From the fact that if Charles were a musician, then Joseph is a mechanic, and that Charles is a musician we can infer that Joseph is a mechanic via modus ponens. Finally, from the fact that if Barbara listens to a song, then Joseph is not a mechanic, and that Joseph is a mechanic we can infer that Barbara is not listening to a song via modus tollens, which contradicts that Barbara is listening to a song. Therefore, the answer is no.