Consider the following premises. If Jessica were a bartender, then it is cloudy. Charles is playing a game. Jennifer is not climbing a mountain. If it is cloudy, then Jennifer is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: Jessica is not a bartender and Charles is playing a game.
 From the fact that if Jessica were a bartender, then it is cloudy, and that if it is cloudy, then Jennifer is climbing a mountain we can infer that if Jessica were a bartender, then Jennifer is climbing a mountain via transitivity. From the fact that if Jessica were a bartender, then Jennifer is climbing a mountain, and that Jennifer is not climbing a mountain we can infer that Jessica is not a bartender via modus tollens. Finally, from the fact that Jessica is not a bartender, and that Charles is playing a game we can infer that Jessica is not a bartender and Charles is playing a game via conjunction. Therefore, the answer is yes.