Translate the following inference to logic notation: For all x, if x_1 makes tea, then x_1 is rich. There is at least one x for which if x_1 were happy, then x_1 is making tea. For all x, x_1 is not rich. Therefore there is at least one x for which x_1 is not happy.
forall x: P(x) -> Q(x). exists x: R(x) -> P(x). forall x: ~Q(x). Therefore exists x: ~R(x).