Translate the following inference to logic notation: For all x, if z_1 were fast, then z_1 is poor. For all x, z_1 will take a plane. There is at least one x for which if z_1 were poor, then z_1 is not taking a plane. For all x, if z_1 were poor, then z_1 is fast. Therefore there is at least one x for which z_1 is not fast.
forall x: P(x) -> Q(x). forall x: R(x). exists x: Q(x) -> ~R(x). forall x: Q(x) -> P(x). Therefore exists x: ~P(x).