Translate the following inference to logic notation: For all x, z is rich or z will not climb a mountain. There is at least one x for which z is rich if and only if z will climb a mountain. Therefore there is at least one x for which z will climb a mountain if and only if z is rich.
forall x: P(x) or ~Q(x). exists x: P(x) <-> Q(x). Therefore exists x: Q(x) <-> P(x).