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