Translate the following inference to logic notation: For all x, if y plays a game, then y is sleeping. There is at least one x for which if y were a politician, then y is playing a game. For all x, y will sleep if and only if y is a politician. Therefore there is at least one x for which y is a politician if and only if y will sleep.
forall x: P(x) -> Q(x). exists x: R(x) -> P(x). forall x: Q(x) <-> R(x). Therefore exists x: R(x) <-> Q(x).