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