Translate the following inference to logic notation: For all x, if x_12 writes a letter, then x_12 is playing tennis. For all x, if x_12 plays tennis, then x_12 is writing a letter. For all x, x_12 is a janitor or x_12 is a doctor. There is at least one x for which x_12 is not a janitor or x_12 will play tennis. For all x, x_12 will write a letter or x_12 is not a doctor. Therefore there is at least one x for which x_12 will write a letter.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: R(x) or S(x). exists x: ~R(x) or Q(x). forall x: P(x) or ~S(x). Therefore exists x: P(x).