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