Translate the following inference to logic notation: For all x, if z were a lawyer, then z is a soldier. For all x, if z were a soldier, then z is a lawyer. For all x, if z were a lawyer, then z is a soldier. Therefore for all x, z is a soldier if and only if z is a lawyer.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: P(x) -> Q(x). Therefore forall x: Q(x) <-> P(x).