Translate the following inference to logic notation: For all x, y will play a game if and only if y is poor. For all x, if y were poor, then y is playing a game. For all x, if y plays a game, then y is poor. Therefore for all x, if y plays a game, then y is poor.
forall x: P(x) <-> Q(x). forall x: Q(x) -> P(x). forall x: P(x) -> Q(x). Therefore forall x: P(x) -> Q(x).