Consider the following premises. David is a police officer if and only if it is cold. Sarah is a soldier or David is not listening to a song. If it is cold, then David is listening to a song. If Joseph were a janitor, then David is a police officer. Can we infer the following from them? If we can, name the inference rule being used: If Joseph were a janitor, then Sarah is a soldier.
 From the fact that David is a police officer if and only if it is cold we can infer that if David were a police officer, then it is cold via biconditional elimination. From the fact that Sarah is a soldier or David is not listening to a song we can infer that if David listens to a song, then Sarah is a soldier via rewriting. From the fact that if David were a police officer, then it is cold, and that if it is cold, then David is listening to a song we can infer that if David were a police officer, then David is listening to a song via transitivity. From the fact that if David were a police officer, then David is listening to a song, and that if David listens to a song, then Sarah is a soldier we can infer that if David were a police officer, then Sarah is a soldier via transitivity. Finally, from the fact that if Joseph were a janitor, then David is a police officer, and that if David were a police officer, then Sarah is a soldier we can infer that if Joseph were a janitor, then Sarah is a soldier via transitivity. Therefore, the answer is yes.