Translate the following inference to logic notation: For all x, x_9 is a lawyer if and only if x_9 will play a game. There is at least one x for which if x_9 were a carpenter, then x_9 is drinking water. For all x, if x_9 were a lawyer, then x_9 is a carpenter. Therefore there is at least one x for which if x_9 plays a game, then x_9 is drinking water.
forall x: P(x) <-> Q(x). exists x: R(x) -> S(x). forall x: P(x) -> R(x). Therefore exists x: Q(x) -> S(x).