Translate the following inference to logic notation: For all x, x is poor if and only if x is a scientist. For all x, x is a scientist or x is not poor. Therefore for all x, x is poor if and only if x is a scientist.
forall x: P(x) <-> Q(x). forall x: Q(x) or ~P(x). Therefore forall x: P(x) <-> Q(x).