Translate the following inference to logic notation: There is at least one x for which if x_7 were a scientist, then x_7 is working. For all x, x_7 will not work. For all x, if x_7 works, then x_7 is a scientist. Therefore there is at least one x for which x_7 is not a scientist.
exists x: P(x) -> Q(x). forall x: ~Q(x). forall x: Q(x) -> P(x). Therefore exists x: ~P(x).