Consider the following premises. David is listening to a song if and only if Linda is a carpenter. If Linda were a carpenter, then David is listening to a song. It is not cold. If it is cold, then David is listening to a song. If David listens to a song, then it is cold. Can we infer the following from them? If we can, name the inference rule being used: Linda is not a carpenter.
 From the fact that if David listens to a song, then it is cold, and that if it is cold, then David is listening to a song we can infer that David is listening to a song if and only if it is cold via biconditional introduction. From the fact that David is listening to a song if and only if Linda is a carpenter we can infer that if David listens to a song, then Linda is a carpenter via biconditional elimination. From the fact that if David listens to a song, then Linda is a carpenter, and that if Linda were a carpenter, then David is listening to a song we can infer that David is listening to a song if and only if Linda is a carpenter via biconditional introduction. From the fact that David is listening to a song if and only if it is cold, and that it is not cold we can infer that David is not listening to a song via biconditional elimination. Finally, from the fact that David is listening to a song if and only if Linda is a carpenter, and that David is not listening to a song we can infer that Linda is not a carpenter via biconditional elimination. Therefore, the answer is yes.