Translate the following inference to logic notation: For all x, x_5 is a doctor or x_5 is a janitor. For all x, x_5 is not a doctor or x_5 will play a game. For all x, x_5 will not play a game. There is at least one x for which x_5 is not a janitor or x_5 will cook. Therefore there is at least one x for which x_5 will cook.
forall x: P(x) or Q(x). forall x: ~P(x) or R(x). forall x: ~R(x). exists x: ~Q(x) or S(x). Therefore exists x: S(x).