Translate the following inference to logic notation: For all x, x_3 is an astronaut or x_3 will not cook. There is at least one x for which x_3 will drive a car if and only if x_3 will cook. Therefore there is at least one x for which if x_3 drives a car, then x_3 is an astronaut.
forall x: P(x) or ~Q(x). exists x: R(x) <-> Q(x). Therefore exists x: R(x) -> P(x).