Translate the following inference to logic notation: There is at least one x for which if z_3 writes a letter, then z_3 is driving a car. For all x, if z_3 drives a car, then z_3 is a scientist. For all x, if z_3 were a scientist, then z_3 is writing a letter. Therefore there is at least one x for which z_3 will drive a car if and only if z_3 will write a letter.
exists x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: R(x) -> P(x). Therefore exists x: Q(x) <-> P(x).