Consider the following premises. If it is late, then it is not cloudy. David is not working. David is working or it is cloudy. Barbara is fast. Can we infer the following from them? If we can, name the inference rule being used: It is late.
 From the fact that David is working or it is cloudy, and that David is not working we can infer that it is cloudy via disjunctive syllogism. Finally, from the fact that if it is late, then it is not cloudy, and that it is cloudy we can infer that it is not late via modus tollens, which contradicts that It is late. Therefore, the answer is no.