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