Translate the following inference to logic notation: For all x, x_8 will not work. There is at least one x for which x_8 is a bartender if and only if x_8 will play squash. For all x, x_8 will cook if and only if x_8 will work. For all x, if x_8 plays squash, then x_8 is cooking. Therefore there is at least one x for which x_8 is not a bartender.
forall x: ~P(x). exists x: Q(x) <-> R(x). forall x: S(x) <-> P(x). forall x: R(x) -> S(x). Therefore exists x: ~Q(x).