Consider the following premises. It is not cold or Charles is reading a book. David is running if and only if Charles is reading a book. It is cold or Jessica is listening to a song. Jessica is not listening to a song. Can we infer the following from them? If we can, name the inference rule being used: David is running.
 From the fact that it is cold or Jessica is listening to a song, and that it is not cold or Charles is reading a book we can infer that Jessica is listening to a song or Charles is reading a book via resolution. From the fact that David is running if and only if Charles is reading a book we can infer that if Charles reads a book, then David is running via biconditional elimination. From the fact that Jessica is listening to a song or Charles is reading a book, and that Jessica is not listening to a song we can infer that Charles is reading a book via disjunctive syllogism. Finally, from the fact that if Charles reads a book, then David is running, and that Charles is reading a book we can infer that David is running via modus ponens. Therefore, the answer is yes.