Translate the following inference to logic notation: For all x, x_5 is a police officer if and only if x_5 is a sailor. For all x, if x_5 were a sailor, then x_5 is playing a game. For all x, if x_5 plays a game, then x_5 is a carpenter. Therefore for all x, if x_5 were a police officer, then x_5 is a carpenter.
forall x: P(x) <-> Q(x). forall x: Q(x) -> R(x). forall x: R(x) -> S(x). Therefore forall x: P(x) -> S(x).