Translate the following inference to logic notation: For all x, if x_1 were a police officer, then x_1 is cooking. For all x, if x_1 goes running, then x_1 is a doctor. For all x, x_1 is a police officer if and only if x_1 is a doctor. Therefore for all x, if x_1 goes running, then x_1 is cooking.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). forall x: P(x) <-> S(x). Therefore forall x: R(x) -> Q(x).