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