Translate the following inference to logic notation: For all x, z_3 will not drive a car. There is at least one x for which z_3 will write a letter if and only if z_3 is poor. For all x, z_3 will drive a car if and only if z_3 is poor. Therefore there is at least one x for which z_3 will not write a letter.
forall x: ~P(x). exists x: Q(x) <-> R(x). forall x: P(x) <-> R(x). Therefore exists x: ~Q(x).