Translate the following inference to logic notation: For all x, x_12 will drive a car if and only if x_12 is a lawyer. For all x, x_12 will listen to a song if and only if x_12 is an office clerk. For all x, if x_12 drives a car, then x_12 is listening to a song. For all x, if x_12 were a doctor, then x_12 is a lawyer. For all x, x_12 is not an office clerk. Therefore for all x, x_12 is not a doctor.
forall x: P(x) <-> Q(x). forall x: R(x) <-> S(x). forall x: P(x) -> R(x). forall x: T(x) -> Q(x). forall x: ~S(x). Therefore forall x: ~T(x).