Consider the following premises. David is not working. Jennifer is rich or Michael is not sleeping. If Jennifer were rich, then David is working. Can we infer the following from them? If we can, name the inference rule being used: Michael is not sleeping.
 From the fact that Jennifer is rich or Michael is not sleeping we can infer that if Michael sleeps, then Jennifer is rich via rewriting. From the fact that if Jennifer were rich, then David is working, and that David is not working we can infer that Jennifer is not rich via modus tollens. Finally, from the fact that if Michael sleeps, then Jennifer is rich, and that Jennifer is not rich we can infer that Michael is not sleeping via modus tollens. Therefore, the answer is yes.