Translate the following inference to logic notation: For all x, if x_3 were happy, then x_3 is playing tennis. For all x, x_3 will play tennis if and only if x_3 is happy. For all x, x_3 is not happy. Therefore for all x, x_3 will not play tennis.
forall x: P(x) -> Q(x). forall x: Q(x) <-> P(x). forall x: ~P(x). Therefore forall x: ~Q(x).