Translate the following inference to logic notation: For all x, if x_2 were sad, then x_2 is a poet. For all x, if x_2 were a doctor, then x_2 is sad. There is at least one x for which if x_2 were a poet, then x_2 is reading a book. Therefore there is at least one x for which if x_2 were a doctor, then x_2 is reading a book.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). exists x: Q(x) -> S(x). Therefore exists x: R(x) -> S(x).