Translate the following inference to logic notation: For all x, if x_2 were happy, then x_2 is a bartender. For all x, if x_2 were a bartender, then x_2 is taking a plane. There is at least one x for which x_2 will not take a plane. Therefore there is at least one x for which x_2 is not happy.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). exists x: ~R(x). Therefore exists x: ~P(x).