Translate the following inference to logic notation: For all x, x_7 is poor or x_7 is a nurse. For all x, x_7 is not poor. There is at least one x for which x_7 will cook or x_7 is not a nurse. Therefore there is at least one x for which x_7 will cook.
forall x: P(x) or Q(x). forall x: ~P(x). exists x: R(x) or ~Q(x). Therefore exists x: R(x).