Translate the following inference to logic notation: For all x, x_5 will not take a plane. For all x, if x_5 climbs a mountain, then x_5 is a carpenter. For all x, if x_5 were a carpenter, then x_5 is taking a plane. For all x, x_5 is a police officer if and only if x_5 will climb a mountain. Therefore for all x, x_5 is not a police officer.
forall x: ~P(x). forall x: Q(x) -> R(x). forall x: R(x) -> P(x). forall x: S(x) <-> Q(x). Therefore forall x: ~S(x).