Translate the following inference to logic notation: For all x, z_3 is a police officer. For all x, if z_3 writes a letter, then z_3 is a police officer. For all x, z_3 will write a letter if and only if z_3 is a police officer. Therefore for all x, z_3 will write a letter.
forall x: P(x). forall x: Q(x) -> P(x). forall x: Q(x) <-> P(x). Therefore forall x: Q(x).