Translate the following inference to logic notation: For all x, y_4 will play a game. For all x, y_4 will not work. For all x, y_4 will work or y is an astronaut. Therefore there is at least one x for which y is an astronaut.
forall x: P(x). forall x: ~Q(x). forall x: Q(x) or R(x). Therefore exists x: R(x).