Translate the following inference to logic notation: For all x, y_4 will write a letter or y_4 will not play a game. There is at least one x for which y_4 is an astronaut if and only if y_4 will write a letter. Therefore there is at least one x for which if y_4 plays a game, then y_4 is an astronaut.
forall x: P(x) or ~Q(x). exists x: R(x) <-> P(x). Therefore exists x: Q(x) -> R(x).