Consider the following premises. If it is cold, then Charles is climbing a mountain. It is sunny. If it is sunny, then it is cold. If it is cloudy, then Charles is not climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: It is cloudy.
 From the fact that if it is sunny, then it is cold, and that if it is cold, then Charles is climbing a mountain we can infer that if it is sunny, then Charles is climbing a mountain via transitivity. From the fact that if it is sunny, then Charles is climbing a mountain, and that it is sunny we can infer that Charles is climbing a mountain via modus ponens. Finally, from the fact that if it is cloudy, then Charles is not climbing a mountain, and that Charles is climbing a mountain we can infer that it is not cloudy via modus tollens, which contradicts that It is cloudy. Therefore, the answer is no.