Translate the following inference to logic notation: For all x, x_9 is a poet or x_9 is not a police officer. There is at least one x for which x_9 will sleep if and only if x_9 is a poet. Therefore there is at least one x for which if x_9 were a police officer, then x_9 is sleeping.
forall x: P(x) or ~Q(x). exists x: R(x) <-> P(x). Therefore exists x: Q(x) -> R(x).