Translate the following inference to logic notation: For all x, if x were a janitor, then x is working. For all x, if x were a doctor, then x is a janitor. For all x, if x were a janitor, then x is a doctor. For all x, if x works, then x is a doctor. Therefore for all x, x is a doctor if and only if x is a janitor.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: P(x) -> R(x). forall x: Q(x) -> R(x). Therefore forall x: R(x) <-> P(x).