Translate the following inference to logic notation: There is at least one x for which if x_5 were a politician, then x_5 is driving a car. For all x, x_5 is a doctor if and only if x_5 is a politician. For all x, if x_5 drives a car, then x_5 is a doctor. Therefore there is at least one x for which x_5 is a politician if and only if x_5 is a doctor.
exists x: P(x) -> Q(x). forall x: R(x) <-> P(x). forall x: Q(x) -> R(x). Therefore exists x: P(x) <-> R(x).