Translate the following inference to logic notation: For all x, if x_5 were a nurse, then x_5 is playing squash. There is at least one x for which if x_5 climbs a mountain, then x_5 is playing squash. For all x, x_5 is a nurse and x_5 will sleep. Therefore there is at least one x for which x_5 will play squash.
forall x: P(x) -> Q(x). exists x: R(x) -> Q(x). forall x: P(x) and S(x). Therefore exists x: Q(x).