Translate the following inference to logic notation: For all x, if y were a poet, then y is climbing a mountain. For all x, if y climbs a mountain, then y is taking a plane. For all x, if y takes a plane, then y is writing a letter. For all x, if y writes a letter, then y is a poet. Therefore for all x, y is a poet if and only if y will write a letter.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: R(x) -> S(x). forall x: S(x) -> P(x). Therefore forall x: P(x) <-> S(x).