Translate the following inference to logic notation: For all x, if z_3 goes running, then z_3 is happy. For all x, z_3 will not go running. For all x, if z_3 goes running, then z_3 is happy. There is at least one x for which if z_3 were happy, then z_3 is running. Therefore there is at least one x for which z_3 is not happy.
forall x: P(x) -> Q(x). forall x: ~P(x). forall x: P(x) -> Q(x). exists x: Q(x) -> P(x). Therefore exists x: ~Q(x).