Consider the following premises. Richard is writing a letter or David is not excited. Richard is writing a letter if and only if David is excited. David is not excited. Can we infer the following from them? Richard is writing a letter.
 From the fact that Richard is writing a letter or David is not excited we can infer that if David were excited, then Richard is writing a letter. From the fact that Richard is writing a letter if and only if David is excited we can infer that if Richard writes a letter, then David is excited. From the fact that if Richard writes a letter, then David is excited, and that if David were excited, then Richard is writing a letter we can infer that Richard is writing a letter if and only if David is excited. Finally, from the fact that Richard is writing a letter if and only if David is excited, and that David is not excited we can infer that Richard is not writing a letter, which contradicts that Richard is writing a letter. Therefore, the answer is no.