Translate the following inference to logic notation: For all x, if x were a lawyer, then x is climbing a mountain. For all x, if x climbs a mountain, then x is a lawyer. Therefore for all x, x will climb a mountain if and only if x is a lawyer.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). Therefore forall x: Q(x) <-> P(x).