Translate the following inference to logic notation: For all x, x will not play a game. There is at least one x for which x is excited or x will play a game. For all x, x is not excited or x is an artist. For all x, x is happy. Therefore there is at least one x for which x is an artist and x is happy.
forall x: ~P(x). exists x: Q(x) or P(x). forall x: ~Q(x) or R(x). forall x: S(x). Therefore exists x: R(x) and S(x).