Translate the following inference to logic notation: There is at least one x for which x_10 will not sleep. For all x, x_10 will sleep or x_10 is a doctor. For all x, if x_10 plays squash, then x_10 is poor. For all x, x_10 will play squash. Therefore there is at least one x for which x_10 is a doctor and x_10 is poor.
exists x: ~P(x). forall x: P(x) or Q(x). forall x: R(x) -> S(x). forall x: R(x). Therefore exists x: Q(x) and S(x).