Consider the following premises. James is a writer if and only if Richard is bored. Richard is not bored. Robert is rich if and only if James is not a writer. Can we infer the following from them? If we can, name the inference rule being used: Robert is not rich.
 From the fact that James is a writer if and only if Richard is bored, and that Richard is not bored we can infer that James is not a writer via biconditional elimination. From the fact that Robert is rich if and only if James is not a writer we can infer that if James were not a writer, then Robert is rich via biconditional elimination. Finally, from the fact that if James were not a writer, then Robert is rich, and that James is not a writer we can infer that Robert is rich via modus ponens, which contradicts that Robert is not rich. Therefore, the answer is no.