Consider the following premises. Jessica is not drinking water. If Barbara climbs a mountain, then Jessica is drinking water. If it snows, then it is cloudy. If Barbara doesn't climb a mountain, then it is snowing. Can we infer the following from them? If we can, name the inference rule being used: It is not cloudy.
 From the fact that if Barbara climbs a mountain, then Jessica is drinking water, and that Jessica is not drinking water we can infer that Barbara is not climbing a mountain via modus tollens. From the fact that if Barbara doesn't climb a mountain, then it is snowing, and that Barbara is not climbing a mountain we can infer that it is snowing via modus ponens. Finally, from the fact that if it snows, then it is cloudy, and that it is snowing we can infer that it is cloudy via modus ponens, which contradicts that It is not cloudy. Therefore, the answer is no.