Translate the following inference to logic notation: For all x, x_2 is not excited or x_2 will cook. There is at least one x for which x_2 is not a janitor or x_2 will play a game. For all x, x_2 is excited or x_2 is a janitor. Therefore there is at least one x for which x_2 will cook or x_2 will play a game.
forall x: ~P(x) or Q(x). exists x: ~R(x) or S(x). forall x: P(x) or R(x). Therefore exists x: Q(x) or S(x).