Translate the following inference to logic notation: For all x, if y climbs a mountain, then y is poor. There is at least one x for which if y were poor, then y is playing squash. For all x, if y plays squash, then y is climbing a mountain. Therefore there is at least one x for which y will climb a mountain if and only if y will play squash.
forall x: P(x) -> Q(x). exists x: Q(x) -> R(x). forall x: R(x) -> P(x). Therefore exists x: P(x) <-> R(x).