Consider the following premises. If David plays a game, then Jennifer is writing a letter. David is a server if and only if Jennifer is writing a letter. For all x_9, x_9 will play a game. Can we infer the following from them? If we can, name the inference rule being used: Jennifer is not writing a letter.
 From the fact that for all x_9, x_9 will play a game we can infer that for all x_9, x_9 will play a game or x_9 is a server via universal addition. From the fact that for all x_9, x_9 will play a game or x_9 is a server we can infer that David is playing a game or David is a server via universal instantiation. From the fact that David is a server if and only if Jennifer is writing a letter we can infer that if David were a server, then Jennifer is writing a letter via biconditional elimination. Finally, from the fact that if David plays a game, then Jennifer is writing a letter, that if David were a server, then Jennifer is writing a letter, and that David is playing a game or David is a server we can infer that Jennifer is writing a letter via disjunction elimination, which contradicts that Jennifer is not writing a letter. Therefore, the answer is no.