Translate the following inference to logic notation: There is at least one x for which x_7 will work. For all x, x_7 will drive a car and x_7 will climb a mountain. For all x, if x_7 works, then x_7 is running. Therefore there is at least one x for which x_7 will drive a car and x_7 will go running.
exists x: P(x). forall x: Q(x) and R(x). forall x: P(x) -> S(x). Therefore exists x: Q(x) and S(x).