Translate the following inference to logic notation: For all x, z_3 is a lawyer if and only if z_3 will write a letter. There is at least one x for which z_3 will write a letter if and only if z_3 is a lawyer. Therefore there is at least one x for which z_3 will write a letter if and only if z_3 is a lawyer.
forall x: P(x) <-> Q(x). exists x: Q(x) <-> P(x). Therefore exists x: Q(x) <-> P(x).