Consider the following premises. Jessica is playing squash or it is not late. Michael is an astronaut or it is late. If Michael were an astronaut, then Jessica is playing squash. Can we infer the following from them? If we can, name the inference rule being used: Jessica is playing squash or it is cloudy.
 From the fact that Jessica is playing squash or it is not late we can infer that if it is late, then Jessica is playing squash via rewriting. From the fact that if Michael were an astronaut, then Jessica is playing squash, that if it is late, then Jessica is playing squash, and that Michael is an astronaut or it is late we can infer that Jessica is playing squash via disjunction elimination. Finally, from the fact that Jessica is playing squash we can infer that Jessica is playing squash or it is cloudy via addition. Therefore, the answer is yes.