Translate the following inference to logic notation: For all x, if x_9 were bored, then x_9 is working. For all x, x_9 is bored if and only if x_9 will listen to a song. There is at least one x for which if x_9 works, then x_9 is an office clerk. Therefore there is at least one x for which if x_9 listens to a song, then x_9 is an office clerk.
forall x: P(x) -> Q(x). forall x: P(x) <-> R(x). exists x: Q(x) -> S(x). Therefore exists x: R(x) -> S(x).