Translate the following inference to logic notation: For all x, if x_9 takes a plane, then x_9 is cooking. For all x, if x_9 climbs a mountain, then x_9 is excited. There is at least one x for which if x_9 cooks, then x_9 is climbing a mountain. For all x, if x_9 were a lawyer, then x_9 is cooking. For all x, x_9 is a lawyer or x_9 will take a plane. Therefore there is at least one x for which x_9 is excited.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). exists x: Q(x) -> R(x). forall x: T(x) -> Q(x). forall x: T(x) or P(x). Therefore exists x: S(x).