Translate the following inference to logic notation: For all x, x_8 will go running if and only if x_8 is a police officer. For all x, x_8 is poor. For all x, if x_8 were sad, then x_8 is running. For all x, x_8 is a police officer or x_8 is sad. Therefore for all x, x_8 will go running and x_8 is poor.
forall x: P(x) <-> Q(x). forall x: R(x). forall x: S(x) -> P(x). forall x: Q(x) or S(x). Therefore forall x: P(x) and R(x).