Translate the following inference to logic notation: For all x, if x_9 cooks, then x_9 is happy. For all x, if x_9 were a bartender, then x_9 is cooking. For all x, x_9 will play squash. For all x, if x_9 plays squash, then x_9 is a bartender. There is at least one x for which x_9 will listen to a song. Therefore there is at least one x for which x_9 is happy and x_9 will listen to a song.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). forall x: S(x). forall x: S(x) -> R(x). exists x: T(x). Therefore exists x: Q(x) and T(x).