Translate the following inference to logic notation: For all x, x_8 will drive a car or x_8 will not cook. There is at least one x for which x_8 will drive a car if and only if x_8 will cook. Therefore there is at least one x for which x_8 will cook if and only if x_8 will drive a car.
forall x: P(x) or ~Q(x). exists x: P(x) <-> Q(x). Therefore exists x: Q(x) <-> P(x).