Translate the following inference to logic notation: For all x, if x_3 were a nurse, then x_3 is playing squash. For all x, if x_3 plays squash, then x_3 is a nurse. There is at least one x for which x_3 will not cook. For all x, if x_3 were a nurse, then x_3 is cooking. Therefore there is at least one x for which x_3 will not play squash.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). exists x: ~R(x). forall x: P(x) -> R(x). Therefore exists x: ~Q(x).