Translate the following inference to logic notation: For all x, x_6 will write a letter or x_6 will work. For all x, if x_6 were excited, then x_6 is playing tennis. For all x, if x_6 were a janitor, then x_6 is playing tennis. There is at least one x for which if x_6 works, then x_6 is excited. For all x, if x_6 writes a letter, then x_6 is a janitor. Therefore there is at least one x for which x_6 will play tennis.
forall x: P(x) or Q(x). forall x: R(x) -> S(x). forall x: T(x) -> S(x). exists x: Q(x) -> R(x). forall x: P(x) -> T(x). Therefore exists x: S(x).