Translate the following inference to logic notation: For all x, y will work if and only if y will climb a mountain. For all x, if y were a carpenter, then y is poor. For all x, if y climbs a mountain, then y is a carpenter. Therefore for all x, if y works, then y is poor.
forall x: P(x) <-> Q(x). forall x: R(x) -> S(x). forall x: Q(x) -> R(x). Therefore forall x: P(x) -> S(x).