Translate the following inference to logic notation: There is at least one x for which x_6 is a doctor if and only if x_6 will play a game. For all x, if x_6 plays a game, then x_6 is a doctor. Therefore there is at least one x for which if x_6 plays a game, then x_6 is a doctor.
exists x: P(x) <-> Q(x). forall x: Q(x) -> P(x). Therefore exists x: Q(x) -> P(x).