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