Translate the following inference to logic notation: For all x, if x_9 were sad, then x_9 is making tea. For all x, x_9 is sad. For all x, if x_9 makes tea, then x_9 is a janitor. For all x, x_9 is a janitor if and only if x_9 will play a game. Therefore for all x, x_9 will play a game.
forall x: P(x) -> Q(x). forall x: P(x). forall x: Q(x) -> R(x). forall x: R(x) <-> S(x). Therefore forall x: S(x).