Translate the following inference to logic notation: For all x, if x_11 plays a game, then x_11 is a politician. For all x, x_11 will play a game or x_11 will drink water. For all x, x_11 is not a politician. There is at least one x for which if x_11 drinks water, then x_11 is a politician. Therefore there is at least one x for which x_11 is excited.
forall x: P(x) -> Q(x). forall x: P(x) or R(x). forall x: ~Q(x). exists x: R(x) -> Q(x). Therefore exists x: S(x).