Consider the following premises. James is an astronaut. If Elisabeth cooks, then James is not an astronaut. If Elisabeth doesn't cook, then Sarah is a server. David is writing a letter. Can we infer the following from them? If we can, name the inference rule being used: Sarah is a server and David is writing a letter.
 From the fact that if Elisabeth cooks, then James is not an astronaut, and that James is an astronaut we can infer that Elisabeth is not cooking via modus tollens. From the fact that if Elisabeth doesn't cook, then Sarah is a server, and that Elisabeth is not cooking we can infer that Sarah is a server via modus ponens. Finally, from the fact that Sarah is a server, and that David is writing a letter we can infer that Sarah is a server and David is writing a letter via conjunction. Therefore, the answer is yes.