Translate the following inference to logic notation: For all x, if y plays tennis, then y is happy. For all x, y will work if and only if y will play tennis. For all x, y is not happy. Therefore for all x, y will not work.
forall x: P(x) -> Q(x). forall x: R(x) <-> P(x). forall x: ~Q(x). Therefore forall x: ~R(x).