Consider the following premises. Elisabeth is not sad. If Michael were an astronaut, then Joseph is playing a game. If Joseph plays a game, then Elisabeth is sad. If Jennifer were a nurse, then Michael is an astronaut. Can we infer the following from them? If we can, name the inference rule being used: Jennifer is not a nurse.
 From the fact that if Jennifer were a nurse, then Michael is an astronaut, and that if Michael were an astronaut, then Joseph is playing a game we can infer that if Jennifer were a nurse, then Joseph is playing a game via transitivity. From the fact that if Joseph plays a game, then Elisabeth is sad, and that Elisabeth is not sad we can infer that Joseph is not playing a game via modus tollens. Finally, from the fact that if Jennifer were a nurse, then Joseph is playing a game, and that Joseph is not playing a game we can infer that Jennifer is not a nurse via modus tollens. Therefore, the answer is yes.