Consider the following premises. If Jennifer were an artist, then Michael is taking a plane. Patricia is happy or Barbara is an electrician. Barbara is not an electrician or Jennifer is an artist. Patricia is not happy or Barbara is an astronaut. If Barbara were an astronaut, then it is cold. If it is cold, then Michael is taking a plane. Can we infer the following from them? If we can, name the inference rule being used: Michael is taking a plane.
 From the fact that if Barbara were an astronaut, then it is cold, and that if it is cold, then Michael is taking a plane we can infer that if Barbara were an astronaut, then Michael is taking a plane via transitivity. From the fact that Patricia is happy or Barbara is an electrician, and that Patricia is not happy or Barbara is an astronaut we can infer that Barbara is an electrician or Barbara is an astronaut via resolution. From the fact that Barbara is an electrician or Barbara is an astronaut, and that Barbara is not an electrician or Jennifer is an artist we can infer that Barbara is an astronaut or Jennifer is an artist via resolution. Finally, from the fact that if Barbara were an astronaut, then Michael is taking a plane, that if Jennifer were an artist, then Michael is taking a plane, and that Barbara is an astronaut or Jennifer is an artist we can infer that Michael is taking a plane via disjunction elimination. Therefore, the answer is yes.