Translate the following inference to logic notation: For all x, x_4 will drive a car if and only if x_4 is a politician. For all x, x_4 will write a letter if and only if x_4 will drive a car. There is at least one x for which if x_4 writes a letter, then x_4 is a politician. Therefore there is at least one x for which if x_4 drives a car, then x_4 is a politician.
forall x: P(x) <-> Q(x). forall x: R(x) <-> P(x). exists x: R(x) -> Q(x). Therefore exists x: P(x) -> Q(x).