Translate the following inference to logic notation: For all x, if x_8 were happy, then x_8 is making tea. There is at least one x for which if x_8 plays a game, then x_8 is not making tea. For all x, x_8 is happy or x_8 is a carpenter. For all x, x_8 will make tea if and only if x_8 is a carpenter. Therefore there is at least one x for which x_8 will not play a game.
forall x: P(x) -> Q(x). exists x: R(x) -> ~Q(x). forall x: P(x) or S(x). forall x: Q(x) <-> S(x). Therefore exists x: ~R(x).