Translate the following inference to logic notation: For all x, if x_13 were rich, then x_13 is playing a game. For all x, x_13 will play squash. For all x, x_13 is rich. There is at least one x for which if x_13 plays a game, then x_13 is writing a letter. Therefore there is at least one x for which x_13 will write a letter.
forall x: P(x) -> Q(x). forall x: R(x). forall x: P(x). exists x: Q(x) -> S(x). Therefore exists x: S(x).