Translate the following inference to logic notation: For all x, x_8 is a server if and only if x_8 is excited. For all x, x_8 is not rich. For all x, x_8 is excited or x_8 is a nurse. For all x, x_8 is a server if and only if x_8 is rich. Therefore for all x, x_8 is a nurse.
forall x: P(x) <-> Q(x). forall x: ~R(x). forall x: Q(x) or S(x). forall x: P(x) <-> R(x). Therefore forall x: S(x).