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