Translate the following inference to logic notation: For all x, y_1 will go running if and only if y_1 will work. For all x, y_1 will play a game if and only if y_1 will go running. Therefore for all x, if y_1 plays a game, then y_1 is working.
forall x: P(x) <-> Q(x). forall x: R(x) <-> P(x). Therefore forall x: R(x) -> Q(x).