Consider the following premises. If Barbara listens to a song, then Jennifer is a scientist. Barbara is listening to a song if and only if Linda is playing tennis. If Jennifer were a scientist, then Barbara is listening to a song. Jennifer is not a scientist. Can we infer the following from them? If we can, name the inference rule being used: Linda is not playing tennis.
 From the fact that if Jennifer were a scientist, then Barbara is listening to a song, and that if Barbara listens to a song, then Jennifer is a scientist we can infer that Jennifer is a scientist if and only if Barbara is listening to a song via biconditional introduction. From the fact that Jennifer is a scientist if and only if Barbara is listening to a song we can infer that if Barbara listens to a song, then Jennifer is a scientist via biconditional elimination. From the fact that if Barbara listens to a song, then Jennifer is a scientist, and that Jennifer is not a scientist we can infer that Barbara is not listening to a song via modus tollens. Finally, from the fact that Barbara is listening to a song if and only if Linda is playing tennis, and that Barbara is not listening to a song we can infer that Linda is not playing tennis via biconditional elimination. Therefore, the answer is yes.