Translate the following inference to logic notation: There is at least one x for which z is curious if and only if z is an astronaut. For all x, z is an astronaut if and only if z is curious. Therefore there is at least one x for which if z were curious, then z is an astronaut.
exists x: P(x) <-> Q(x). forall x: Q(x) <-> P(x). Therefore exists x: P(x) -> Q(x).