Consider the following premises. If Barbara listens to a song, then Robert is writing a letter. Sarah is reading a book. If Robert writes a letter, then Sarah is not reading a book. Can we infer the following from them? If we can, name the inference rule being used: Barbara is not listening to a song or Joseph is a sailor.
 From the fact that if Robert writes a letter, then Sarah is not reading a book, and that Sarah is reading a book we can infer that Robert is not writing a letter via modus tollens. From the fact that if Barbara listens to a song, then Robert is writing a letter, and that Robert is not writing a letter we can infer that Barbara is not listening to a song via modus tollens. Finally, from the fact that Barbara is not listening to a song we can infer that Barbara is not listening to a song or Joseph is a sailor via addition. Therefore, the answer is yes.