Translate the following inference to logic notation: For all x, if x_10 plays tennis, then x_10 is working. There is at least one x for which x_10 will not work. For all x, if x_10 works, then x_10 is a nurse. For all x, x_10 will climb a mountain if and only if x_10 will play tennis. For all x, if x_10 were a nurse, then x_10 is playing tennis. Therefore there is at least one x for which x_10 will not climb a mountain.
forall x: P(x) -> Q(x). exists x: ~Q(x). forall x: Q(x) -> R(x). forall x: S(x) <-> P(x). forall x: R(x) -> P(x). Therefore exists x: ~S(x).