Translate the following inference to logic notation: For all x, if z_2 drives a car, then z_2 is happy. There is at least one x for which z_2 will drive a car if and only if z_2 is a cashier. For all x, if z_2 were happy, then z_2 is driving a car. For all x, z_2 is not a cashier. Therefore there is at least one x for which z_2 is not happy.
forall x: P(x) -> Q(x). exists x: P(x) <-> R(x). forall x: Q(x) -> P(x). forall x: ~R(x). Therefore exists x: ~Q(x).