Translate the following inference to logic notation: For all x, if x_9 were an office clerk, then x_9 is happy. For all x, if x_9 were happy, then x_9 is an office clerk. For all x, if x_9 were happy, then x_9 is playing tennis. 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 works, then x_9 is playing tennis.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: Q(x) -> R(x). exists x: S(x) -> P(x). Therefore exists x: S(x) -> R(x).