Consider the following premises. For all x, x is a nurse if and only if x will read a book. For all x, x is a soldier if and only if x will read a book. For all x, if x were a soldier, then x is a nurse. Can we infer the following from them? There is at least one x for which the fact that x were a nurse does not imply that x is a soldier.
 From the fact that for all x, x is a nurse if and only if x will read a book we can infer that for all x, if x were a nurse, then x is reading a book. From the fact that for all x, x is a soldier if and only if x will read a book we can infer that for all x, if x reads a book, then x is a soldier. From the fact that for all x, if x were a nurse, then x is reading a book, and that for all x, if x reads a book, then x is a soldier we can infer that for all x, if x were a nurse, then x is a soldier. From the fact that for all x, if x were a nurse, then x is a soldier, and that for all x, if x were a soldier, then x is a nurse we can infer that for all x, x is a nurse if and only if x is a soldier. Finally, from the fact that for all x, x is a nurse if and only if x is a soldier we can infer that for all x, if x were a nurse, then x is a soldier, which contradicts that There is at least one x for which the fact that x were a nurse does not imply that x is a soldier. Therefore, the answer is no.