Translate the following inference to logic notation: There is at least one x for which if y_2 were a cashier, then y_2 is a janitor. For all x, if y_2 were a nurse, then y_2 is a police officer. For all x, if y_2 were a janitor, then y_2 is a nurse. For all x, if y_2 were a police officer, then y_2 is a cashier. Therefore there is at least one x for which y_2 is a police officer if and only if y_2 is a janitor.
exists x: P(x) -> Q(x). forall x: R(x) -> S(x). forall x: Q(x) -> R(x). forall x: S(x) -> P(x). Therefore exists x: S(x) <-> Q(x).