Consider the following premises. James is not a carpenter. If David were a lawyer, then James is a carpenter. If it is cloudy, then David is a lawyer. 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 cloudy, then David is a lawyer, and that if David were a lawyer, then James is a carpenter we can infer that if it is cloudy, then James is a carpenter via transitivity. Finally, from the fact that if it is cloudy, then James is a carpenter, and that James is not a carpenter we can infer that it is not cloudy via modus tollens, which contradicts that It is cloudy. Therefore, the answer is no.