Consider the following premises. Jennifer is not fast. If Joseph works, then Linda is rich. If Linda were rich, then it is cloudy. Jennifer is fast or it is not cloudy. Can we infer the following from them? If we can, name the inference rule being used: Joseph is not working.
 From the fact that Jennifer is fast or it is not cloudy we can infer that if it is cloudy, then Jennifer is fast via rewriting. From the fact that if Linda were rich, then it is cloudy, and that if it is cloudy, then Jennifer is fast we can infer that if Linda were rich, then Jennifer is fast via transitivity. From the fact that if Linda were rich, then Jennifer is fast, and that Jennifer is not fast we can infer that Linda is not rich via modus tollens. Finally, from the fact that if Joseph works, then Linda is rich, and that Linda is not rich we can infer that Joseph is not working via modus tollens. Therefore, the answer is yes.