Translate the following inference to logic notation: For all x, x_4 will work or x_4 is not a scientist. There is at least one x for which if x_4 works, then x_4 is a scientist. For all x, x_4 is not a scientist. Therefore there is at least one x for which x_4 will not work.
forall x: P(x) or ~Q(x). exists x: P(x) -> Q(x). forall x: ~Q(x). Therefore exists x: ~P(x).