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