Consider the following premises. If Charles listens to a song, then Linda is a taxi driver. If Linda were a taxi driver, then William is writing a letter. Charles is listening to a song if and only if William is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: William is writing a letter if and only if Charles is listening to a song.
 From the fact that if Charles listens to a song, then Linda is a taxi driver, and that if Linda were a taxi driver, then William is writing a letter we can infer that if Charles listens to a song, then William is writing a letter via transitivity. From the fact that Charles is listening to a song if and only if William is writing a letter we can infer that if William writes a letter, then Charles is listening to a song via biconditional elimination. Finally, from the fact that if William writes a letter, then Charles is listening to a song, and that if Charles listens to a song, then William is writing a letter we can infer that William is writing a letter if and only if Charles is listening to a song via biconditional introduction. Therefore, the answer is yes.