Translate the following inference to logic notation: For all x, x_8 is a nurse if and only if x_8 will play a game. For all x, x_8 will play a game if and only if x_8 will drink water. There is at least one x for which x_8 will not drink water. Therefore there is at least one x for which x_8 is not a nurse.
forall x: P(x) <-> Q(x). forall x: Q(x) <-> R(x). exists x: ~R(x). Therefore exists x: ~P(x).