Consider the following premises. Mary is listening to a song or David is playing tennis. If David plays tennis, then it is sunny. David is playing tennis or it is not sunny. Mary is not listening to a song or it is overcast. It is not sunny. Can we infer the following from them? If we can, name the inference rule being used: It is overcast.
 From the fact that Mary is listening to a song or David is playing tennis, and that Mary is not listening to a song or it is overcast we can infer that David is playing tennis or it is overcast via resolution. From the fact that David is playing tennis or it is not sunny we can infer that if it is sunny, then David is playing tennis via rewriting. From the fact that if it is sunny, then David is playing tennis, and that if David plays tennis, then it is sunny we can infer that it is sunny if and only if David is playing tennis via biconditional introduction. From the fact that it is sunny if and only if David is playing tennis, and that it is not sunny we can infer that David is not playing tennis via biconditional elimination. Finally, from the fact that David is playing tennis or it is overcast, and that David is not playing tennis we can infer that it is overcast via disjunctive syllogism. Therefore, the answer is yes.