Translate the following inference to logic notation: For all x, if x_9 plays squash, then x_9 is working. For all x, x_9 will play squash or x_9 is a janitor. There is at least one x for which x_9 will work if and only if x_9 is a nurse. For all x, if x_9 were a janitor, then x_9 is a nurse. Therefore there is at least one x for which x_9 is a nurse.
forall x: P(x) -> Q(x). forall x: P(x) or R(x). exists x: Q(x) <-> S(x). forall x: R(x) -> S(x). Therefore exists x: S(x).