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