Translate the following inference to logic notation: For all x, x_12 will write a letter and x_12 is an office clerk. There is at least one x for which x_12 is not rich. For all x, x_12 is rich or x_12 is a doctor. Therefore there is at least one x for which x_12 is a doctor and x_12 will write a letter.
forall x: P(x) and Q(x). exists x: ~R(x). forall x: R(x) or S(x). Therefore exists x: S(x) and P(x).