Consider the following premises. If David were a nurse, then David is not playing a game. If Mary works, then David is a nurse. If Charles writes a letter, then Mary is working. David is playing a game. Charles is writing a letter or Mary is not working. Can we infer the following from them? Charles is writing a letter.
 From the fact that Charles is writing a letter or Mary is not working we can infer that if Mary works, then Charles is writing a letter. From the fact that if David were a nurse, then David is not playing a game, and that David is playing a game we can infer that David is not a nurse. From the fact that if Charles writes a letter, then Mary is working, and that if Mary works, then Charles is writing a letter we can infer that Charles is writing a letter if and only if Mary is working. From the fact that if Mary works, then David is a nurse, and that David is not a nurse we can infer that Mary is not working. Finally, from the fact that Charles is writing a letter if and only if Mary is working, and that Mary is not working we can infer that Charles is not writing a letter, which contradicts that Charles is writing a letter. Therefore, the answer is no.