Translate the following inference to logic notation: For all x, x_4 will take a plane if and only if x_4 will drive a car. John is driving a car if and only if John is taking a plane. Therefore John is taking a plane if and only if John is driving a car.
forall x: P(x) <-> Q(x). Q(a) <-> P(a). Therefore P(a) <-> Q(a).