Translate the following inference to logic notation: For all x, x is a nurse if and only if x is a soldier. For all x, x is a soldier if and only if x is a nurse. There is at least one x for which if x were a soldier, then x is a nurse. Therefore there is at least one x for which x is a soldier if and only if x is a nurse.
forall x: P(x) <-> Q(x). forall x: Q(x) <-> P(x). exists x: Q(x) -> P(x). Therefore exists x: Q(x) <-> P(x).