Consider the following premises. If James writes a letter, then Joseph is a janitor. Joseph is not a janitor. James is writing a letter if and only if it is cloudy. Can we infer the following from them? If we can, name the inference rule being used: It is cloudy.
 From the fact that if James writes a letter, then Joseph is a janitor, and that Joseph is not a janitor we can infer that James is not writing a letter via modus tollens. Finally, from the fact that James is writing a letter if and only if it is cloudy, and that James is not writing a letter we can infer that it is not cloudy via biconditional elimination, which contradicts that It is cloudy. Therefore, the answer is no.