Translate the following inference to logic notation: There is at least one x for which x_8 will go running if and only if x_8 is a nurse. For all x, if x_8 goes running, then x_8 is happy. For all x, x_8 is happy if and only if x_8 will work. For all x, x_8 will not work. Therefore there is at least one x for which x_8 is not a nurse.
exists x: P(x) <-> Q(x). forall x: P(x) -> R(x). forall x: R(x) <-> S(x). forall x: ~S(x). Therefore exists x: ~Q(x).