Translate the following inference to logic notation: For all x, if x_7 were an electrician, then x_7 is happy. For all x, if x_7 plays a game, then x_7 is an electrician. There is at least one x for which if x_7 were happy, then x_7 is poor. For all x, x_7 is not poor. Therefore there is at least one x for which x_7 will not play a game.
forall x: P(x) -> Q(x). forall x: R(x) -> P(x). exists x: Q(x) -> S(x). forall x: ~S(x). Therefore exists x: ~R(x).