Translate the following inference to logic notation: For all x, x_9 is a politician or x_9 is a police officer. For all x, x_9 is a politician if and only if x_9 is a carpenter. For all x, if x_9 were a carpenter, then x_9 is a police officer. For all x, if x_9 were a police officer, then x_9 is a carpenter. Therefore for all x, x_9 is a carpenter.
forall x: P(x) or Q(x). forall x: P(x) <-> R(x). forall x: R(x) -> Q(x). forall x: Q(x) -> R(x). Therefore forall x: R(x).