Translate the following inference to logic notation: For all x, if x_5 were a carpenter, then x_5 is fast. For all x, if x_5 were fast, then x_5 is a carpenter. For all x, x_5 is fast or x_5 is a police officer. For all x, if x_5 were a police officer, then x_5 is a carpenter. Therefore for all x, x_5 is a carpenter.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: Q(x) or R(x). forall x: R(x) -> P(x). Therefore forall x: P(x).