Translate the following inference to logic notation: For all x, x_6 is happy. For all x, if x_6 were a doctor, then x_6 is taking a plane. There is at least one x for which if x_6 takes a plane, then x_6 is a janitor. For all x, if x_6 were happy, then x_6 is a doctor. Therefore there is at least one x for which x_6 is a janitor.
forall x: P(x). forall x: Q(x) -> R(x). exists x: R(x) -> S(x). forall x: P(x) -> Q(x). Therefore exists x: S(x).