Translate the following inference to logic notation: For all x, x_6 is a doctor. For all x, x_6 is happy or x_6 is sad. For all x, if x_6 were happy, then x_6 is not a doctor. Therefore for all x, x_6 is sad or x_6 is rich.
forall x: P(x). forall x: Q(x) or R(x). forall x: Q(x) -> ~P(x). Therefore forall x: R(x) or S(x).