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