Translate the following inference to logic notation: For all x, z is not a bartender. For all x, if z plays squash, then z is a bartender. There is at least one x for which if z were a bartender, then z is playing squash. For all x, z will play squash or z is not a bartender. Therefore there is at least one x for which z will not play squash.
forall x: ~P(x). forall x: Q(x) -> P(x). exists x: P(x) -> Q(x). forall x: Q(x) or ~P(x). Therefore exists x: ~Q(x).