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