Translate the following inference to logic notation: For all x, x_9 is a janitor. There is at least one x for which x_9 is a nurse or x_9 will cook. For all x, if x_9 cooks, then x_9 is playing tennis. For all x, if x_9 were a nurse, then x_9 is playing tennis. Therefore there is at least one x for which x_9 will play tennis and x_9 is a janitor.
forall x: P(x). exists x: Q(x) or R(x). forall x: R(x) -> S(x). forall x: Q(x) -> S(x). Therefore exists x: S(x) and P(x).