Translate the following inference to logic notation: For all x, x_5 will play a game or x_5 is a soldier. For all x, if x_5 plays a game, then x_5 is a police officer. For all x, x_5 is excited. For all x, if x_5 were a soldier, then x_5 is a police officer. Therefore for all x, x_5 is excited.
forall x: P(x) or Q(x). forall x: P(x) -> R(x). forall x: S(x). forall x: Q(x) -> R(x). Therefore forall x: S(x).