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