Consider the following premises. If it is overcast, then Michael is working. David is taking a plane or it is overcast. It is sunny or David is not taking a plane. If it is sunny, then Michael is working. Can we infer the following from them? If we can, name the inference rule being used: Michael is not working.
 From the fact that it is sunny or David is not taking a plane we can infer that if David takes a plane, then it is sunny via rewriting. From the fact that if David takes a plane, then it is sunny, and that if it is sunny, then Michael is working we can infer that if David takes a plane, then Michael is working via transitivity. Finally, from the fact that if David takes a plane, then Michael is working, that if it is overcast, then Michael is working, and that David is taking a plane or it is overcast we can infer that Michael is working via disjunction elimination, which contradicts that Michael is not working. Therefore, the answer is no.