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