Translate the following inference to logic notation: For all x, if x_5 were rich, then x_5 is an astronaut. For all x, x_5 is rich. For all x, if x_5 were an astronaut, then x_5 is playing a game. For all x, if x_5 plays a game, then x_5 is happy. Therefore for all x, x_5 is happy.
forall x: P(x) -> Q(x). forall x: P(x). forall x: Q(x) -> R(x). forall x: R(x) -> S(x). Therefore forall x: S(x).