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