Translate the following inference to logic notation: For all x, x_5 will not play squash. For all x, x_5 is a nurse if and only if x_5 will play squash. There is at least one x for which if x_5 plays squash, then x_5 is a nurse. Therefore there is at least one x for which x_5 is not a nurse.
forall x: ~P(x). forall x: Q(x) <-> P(x). exists x: P(x) -> Q(x). Therefore exists x: ~Q(x).