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