Translate the following inference to logic notation: There is at least one x for which x_12 is poor or x_12 is not a bartender. For all x, if x_12 plays a game, then x_12 is poor. For all x, if x_12 were poor, then x_12 is playing a game. For all x, if x_12 plays a game, then x_12 is a bartender. Therefore there is at least one x for which x_12 is poor if and only if x_12 is a bartender.
exists x: P(x) or ~Q(x). forall x: R(x) -> P(x). forall x: P(x) -> R(x). forall x: R(x) -> Q(x). Therefore exists x: P(x) <-> Q(x).