Translate the following inference to logic notation: For all x, if y_3 were a soldier, then y_3 is a sailor. For all x, if y_3 were a sailor, then y_3 is playing a game. There is at least one x for which y_3 is a soldier or y_3 will not play a game. Therefore there is at least one x for which y_3 is a soldier if and only if y_3 will play a game.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). exists x: P(x) or ~R(x). Therefore exists x: P(x) <-> R(x).