Consider the following premises. If Patricia were poor, then Jessica is a janitor. David is writing a letter or Jessica is not a janitor. If David writes a letter, then Patricia is poor. Can we infer the following from them? If we can, name the inference rule being used: The fact that Jessica were a janitor does not imply that Patricia is poor.
 From the fact that David is writing a letter or Jessica is not a janitor we can infer that if Jessica were a janitor, then David is writing a letter via rewriting. Finally, from the fact that if Jessica were a janitor, then David is writing a letter, and that if David writes a letter, then Patricia is poor we can infer that if Jessica were a janitor, then Patricia is poor via transitivity, which contradicts that The fact that Jessica were a janitor does not imply that Patricia is poor. Therefore, the answer is no.