Translate the following inference to logic notation: For all x, x_5 is poor. For all x, if x_5 were poor, then x_5 is a doctor. For all x, x_5 is happy. For all x, if x_5 goes running, then x_5 is a doctor. Therefore for all x, x_5 is a doctor and x_5 is happy.
forall x: P(x). forall x: P(x) -> Q(x). forall x: R(x). forall x: S(x) -> Q(x). Therefore forall x: Q(x) and R(x).