Translate the following inference to logic notation: For all x, x_8 is excited or x_8 will read a book. For all x, x_8 will climb a mountain. For all x, if x_8 were excited, then x_8 is cooking. There is at least one x for which if x_8 reads a book, then x_8 is cooking. Therefore there is at least one x for which x_8 will climb a mountain and x_8 will cook.
forall x: P(x) or Q(x). forall x: R(x). forall x: P(x) -> S(x). exists x: Q(x) -> S(x). Therefore exists x: R(x) and S(x).