Translate the following inference to logic notation: For all x, x_10 will cook. There is at least one x for which if x_10 cooks, then x_10 is rich. For all x, if x_10 reads a book, then x_10 is rich. For all x, x_10 is a doctor. Therefore there is at least one x for which x_10 is rich and x_10 is a doctor.
forall x: P(x). exists x: P(x) -> Q(x). forall x: R(x) -> Q(x). forall x: S(x). Therefore exists x: Q(x) and S(x).