Translate the following inference to logic notation: There is at least one x for which x_9 is a police officer if and only if x_9 will go running. For all x, x_9 will play squash if and only if x_9 is a police officer. Therefore there is at least one x for which if x_9 goes running, then x_9 is playing squash.
exists x: P(x) <-> Q(x). forall x: R(x) <-> P(x). Therefore exists x: Q(x) -> R(x).