Consider the following premises. It is not late. Susan is playing a game if and only if David is reading a book. It is late if and only if David is reading a book. Susan is playing a game if and only if Karen is a soldier. Can we infer the following from them? If we can, name the inference rule being used: Karen is a soldier.
 From the fact that it is late if and only if David is reading a book, and that it is not late we can infer that David is not reading a book via biconditional elimination. From the fact that Susan is playing a game if and only if David is reading a book, and that David is not reading a book we can infer that Susan is not playing a game via biconditional elimination. Finally, from the fact that Susan is playing a game if and only if Karen is a soldier, and that Susan is not playing a game we can infer that Karen is not a soldier via biconditional elimination, which contradicts that Karen is a soldier. Therefore, the answer is no.