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