Translate the following inference to logic notation: For all x, z_2 is excited if and only if z_2 is a police officer. For all x, z_2 is not a carpenter. For all x, z_2 is a police officer if and only if z_2 is a carpenter. For all x, if z_2 were a carpenter, then z_2 is a police officer. Therefore for all x, z_2 is not excited.
forall x: P(x) <-> Q(x). forall x: ~R(x). forall x: Q(x) <-> R(x). forall x: R(x) -> Q(x). Therefore forall x: ~P(x).