Consider the following premises. David is a writer if and only if Susan is playing a game. David is a writer if and only if Susan is playing a game. Can we infer the following from them? If we can, name the inference rule being used: If is not true that Susan is playing a game if and only if David is a writer.
 From the fact that David is a writer if and only if Susan is playing a game we can infer that if David were a writer, then Susan is playing a game via biconditional elimination. From the fact that David is a writer if and only if Susan is playing a game we can infer that if Susan plays a game, then David is a writer via biconditional elimination. Finally, from the fact that if Susan plays a game, then David is a writer, and that if David were a writer, then Susan is playing a game we can infer that Susan is playing a game if and only if David is a writer via biconditional introduction, which contradicts that If is not true that Susan is playing a game if and only if David is a writer. Therefore, the answer is no.