Translate the following inference to logic notation: For all x, if y were an astronaut, then y is running. For all x, if y were a janitor, then y is an astronaut. For all x, if y goes running, then y is a janitor. Therefore for all x, y is a janitor if and only if y will go running.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: Q(x) -> R(x). Therefore forall x: R(x) <-> Q(x).