Translate the following inference to logic notation: For all x, x_13 is not sad. For all x, x_13 will work if and only if x_13 will play tennis. For all x, x_13 is rich if and only if x_13 will work. There is at least one x for which x_13 is sad if and only if x_13 is rich. Therefore there is at least one x for which x_13 will not play tennis.
forall x: ~P(x). forall x: Q(x) <-> R(x). forall x: S(x) <-> Q(x). exists x: P(x) <-> S(x). Therefore exists x: ~R(x).