Translate the following inference to logic notation: For all x, x_3 will write a letter. There is at least one x for which if x_3 were poor, then x_3 is a doctor. For all x, if x_3 writes a letter, then x_3 is playing a game. For all x, if x_3 plays a game, then x_3 is a doctor. Therefore there is at least one x for which x_3 is a doctor.
forall x: P(x). exists x: Q(x) -> R(x). forall x: P(x) -> S(x). forall x: S(x) -> R(x). Therefore exists x: R(x).