Consider the following premises. If Charles plays tennis, then Karen is not cooking. If Barbara goes running, then Charles is happy. If Charles doesn't play tennis, then Barbara is running. Karen is cooking. Can we infer the following from them? If we can, name the inference rule being used: Charles is happy.
 From the fact that if Charles plays tennis, then Karen is not cooking, and that Karen is cooking we can infer that Charles is not playing tennis via modus tollens. From the fact that if Charles doesn't play tennis, then Barbara is running, and that if Barbara goes running, then Charles is happy we can infer that if Charles doesn't play tennis, then Charles is happy via transitivity. Finally, from the fact that if Charles doesn't play tennis, then Charles is happy, and that Charles is not playing tennis we can infer that Charles is happy via modus ponens. Therefore, the answer is yes.