Translate the following inference to logic notation: For all x, if y plays a game, then y is writing a letter. For all x, if y writes a letter, then y is playing a game. For all x, if y writes a letter, then y is playing a game. Therefore for all x, if y writes a letter, then y is playing a game.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: Q(x) -> P(x). Therefore forall x: Q(x) -> P(x).