Translate the following inference to logic notation: For all x, x_9 is not happy. For all x, if x_9 writes a letter, then x_9 is a scientist. There is at least one x for which if x_9 writes a letter, then x_9 is happy. For all x, if x_9 were a scientist, then x_9 is writing a letter. Therefore there is at least one x for which x_9 is not a scientist.
forall x: ~P(x). forall x: Q(x) -> R(x). exists x: Q(x) -> P(x). forall x: R(x) -> Q(x). Therefore exists x: ~R(x).