Consider the following premises. If Richard were a mechanic, then Linda is working. It is not overcast. Richard is a mechanic or David is listening to a song. If Linda works, then it is overcast. Can we infer the following from them? If we can, name the inference rule being used: David is not listening to a song.
 From the fact that if Linda works, then it is overcast, and that it is not overcast we can infer that Linda is not working via modus tollens. From the fact that if Richard were a mechanic, then Linda is working, and that Linda is not working we can infer that Richard is not a mechanic via modus tollens. Finally, from the fact that Richard is a mechanic or David is listening to a song, and that Richard is not a mechanic we can infer that David is listening to a song via disjunctive syllogism, which contradicts that David is not listening to a song. Therefore, the answer is no.