Translate the following inference to logic notation: For all x, y_3 will play a game if and only if y_3 will write a letter. For all x, if y_3 writes a letter, then y_3 is fast. For all x, y_3 will play a game or y_3 is not fast. Therefore for all x, y_3 will play a game if and only if y_3 will write a letter.
forall x: P(x) <-> Q(x). forall x: Q(x) -> R(x). forall x: P(x) or ~R(x). Therefore forall x: P(x) <-> Q(x).