Consider the following premises. Joseph is listening to a song. Jennifer is writing a letter or Joseph is not listening to a song. Can we infer the following from them? If we can, name the inference rule being used: Jennifer is not writing a letter.
 From the fact that Jennifer is writing a letter or Joseph is not listening to a song we can infer that if Joseph listens to a song, then Jennifer is writing a letter via rewriting. Finally, from the fact that if Joseph listens to a song, then Jennifer is writing a letter, and that Joseph is listening to a song we can infer that Jennifer is writing a letter via modus ponens, which contradicts that Jennifer is not writing a letter. Therefore, the answer is no.