Translate the following inference to logic notation: For all x, if x were a carpenter, then x is fast. For all x, x is a janitor. For all x, if x were fast, then x is listening to a song. There is at least one x for which if x were a janitor, then x is listening to a song. Therefore there is at least one x for which x will listen to a song.
forall x: P(x) -> Q(x). forall x: R(x). forall x: Q(x) -> S(x). exists x: R(x) -> S(x). Therefore exists x: S(x).