Translate the following inference to logic notation: For all x, if x goes running, then x is cooking. There is at least one x for which x is a nurse or x will not cook. For all x, if x drives a car, then x is running. Therefore there is at least one x for which if x drives a car, then x is a nurse.
forall x: P(x) -> Q(x). exists x: R(x) or ~Q(x). forall x: S(x) -> P(x). Therefore exists x: S(x) -> R(x).