Translate the following inference to logic notation: For all x, if x_6 plays a game, then x_6 is working. For all x, if x_6 works, then x_6 is a janitor. For all x, x_6 will play a game or x_6 is a janitor. There is at least one x for which if x_6 were a janitor, then x_6 is working. Therefore there is at least one x for which x_6 will work.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: P(x) or R(x). exists x: R(x) -> Q(x). Therefore exists x: Q(x).