Consider the following premises. If Thomas goes running, then Richard is poor. Richard is making tea. If Richard were poor, then Jessica is a police officer. If Richard makes tea, then Thomas is running. Can we infer the following from them? If we can, name the inference rule being used: Jessica is not a police officer.
 From the fact that if Richard makes tea, then Thomas is running, and that if Thomas goes running, then Richard is poor we can infer that if Richard makes tea, then Richard is poor via transitivity. From the fact that if Richard makes tea, then Richard is poor, and that Richard is making tea we can infer that Richard is poor via modus ponens. Finally, from the fact that if Richard were poor, then Jessica is a police officer, and that Richard is poor we can infer that Jessica is a police officer via modus ponens, which contradicts that Jessica is not a police officer. Therefore, the answer is no.