Consider the following premises. Joseph is working. If Joseph works, then Elisabeth is sleeping. If Elisabeth sleeps, then Jessica is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: Jessica is not writing a letter.
 From the fact that if Joseph works, then Elisabeth is sleeping, and that Joseph is working we can infer that Elisabeth is sleeping via modus ponens. Finally, from the fact that if Elisabeth sleeps, then Jessica is writing a letter, and that Elisabeth is sleeping we can infer that Jessica is writing a letter via modus ponens, which contradicts that Jessica is not writing a letter. Therefore, the answer is no.