Translate the following inference to logic notation: For all x, x_8 is rich if and only if x_8 will sleep. For all x, x_8 will sleep or x will work. For all x, x_8 is not rich. Therefore there is at least one x for which x will work.
forall x: P(x) <-> Q(x). forall x: Q(x) or R(x). forall x: ~P(x). Therefore exists x: R(x).