Consider the following premises. If Karen were a server, then Karen is poor. Karen is not poor. For all x_12, if x_12 were poor, then x_12 is a server. If Charles were excited, then Karen is a server. Can we infer the following from them? If we can, name the inference rule being used: Charles is not excited.
 From the fact that for all x_12, if x_12 were poor, then x_12 is a server we can infer that if Karen were poor, then Karen is a server via universal instantiation. From the fact that if Karen were poor, then Karen is a server, and that if Karen were a server, then Karen is poor we can infer that Karen is poor if and only if Karen is a server via biconditional introduction. From the fact that Karen is poor if and only if Karen is a server, and that Karen is not poor we can infer that Karen is not a server via biconditional elimination. Finally, from the fact that if Charles were excited, then Karen is a server, and that Karen is not a server we can infer that Charles is not excited via modus tollens. Therefore, the answer is yes.