Consider the following premises. If William were excited, then it is cloudy. If Sarah reads a book, then William is excited. James is writing a letter if and only if Sarah is reading a book. Can we infer the following from them? If we can, name the inference rule being used: The fact that James writes a letter does not imply that it is cloudy.
 From the fact that James is writing a letter if and only if Sarah is reading a book we can infer that if James writes a letter, then Sarah is reading a book via biconditional elimination. From the fact that if James writes a letter, then Sarah is reading a book, and that if Sarah reads a book, then William is excited we can infer that if James writes a letter, then William is excited via transitivity. Finally, from the fact that if James writes a letter, then William is excited, and that if William were excited, then it is cloudy we can infer that if James writes a letter, then it is cloudy via transitivity, which contradicts that The fact that James writes a letter does not imply that it is cloudy. Therefore, the answer is no.