Consider the following premises. If Jennifer were a carpenter, then John is a lawyer. Sarah is a scientist. John is not a lawyer. If Jennifer were not a carpenter, then it is cloudy. Can we infer the following from them? If we can, name the inference rule being used: It is cloudy and Sarah is a scientist.
 From the fact that if Jennifer were a carpenter, then John is a lawyer, and that John is not a lawyer we can infer that Jennifer is not a carpenter via modus tollens. From the fact that if Jennifer were not a carpenter, then it is cloudy, and that Jennifer is not a carpenter we can infer that it is cloudy via modus ponens. Finally, from the fact that it is cloudy, and that Sarah is a scientist we can infer that it is cloudy and Sarah is a scientist via conjunction. Therefore, the answer is yes.