Translate the following inference to logic notation: For all x, if x_10 were a writer, then x_10 is poor. For all x, if x_10 cooks, then x_10 is running. There is at least one x for which if x_10 goes running, then x_10 is cooking. For all x, x_10 is not poor. For all x, x_10 will go running if and only if x_10 is a writer. Therefore there is at least one x for which x_10 will not cook.
forall x: P(x) -> Q(x). forall x: R(x) -> S(x). exists x: S(x) -> R(x). forall x: ~Q(x). forall x: S(x) <-> P(x). Therefore exists x: ~R(x).