Translate the following inference to logic notation: For all x, x_3 will play squash. For all x, if x_3 plays squash, then x_3 is cooking. There is at least one x for which if x_3 were fast, then x_3 is taking a plane. For all x, if x_3 cooks, then x_3 is taking a plane. Therefore there is at least one x for which x_3 will take a plane.
forall x: P(x). forall x: P(x) -> Q(x). exists x: R(x) -> S(x). forall x: Q(x) -> S(x). Therefore exists x: S(x).