Consider the following premises. If Charles writes a letter, then Karen is a janitor. Charles is writing a letter or Karen is not a janitor. Charles is not writing a letter. Can we infer the following from them? If we can, name the inference rule being used: Karen is a janitor.
 From the fact that Charles is writing a letter or Karen is not a janitor we can infer that if Karen were a janitor, then Charles is writing a letter via rewriting. From the fact that if Charles writes a letter, then Karen is a janitor, and that if Karen were a janitor, then Charles is writing a letter we can infer that Charles is writing a letter if and only if Karen is a janitor via biconditional introduction. Finally, from the fact that Charles is writing a letter if and only if Karen is a janitor, and that Charles is not writing a letter we can infer that Karen is not a janitor via biconditional elimination, which contradicts that Karen is a janitor. Therefore, the answer is no.