Translate the following inference to logic notation: If Elisabeth were a lawyer, then William is happy. For all x, if x_15 works, then x_15 is a janitor. If Michael were poor, then Barbara is working. If Barbara were a janitor, then Michael is playing a game. If William were happy, then Michael is poor. Therefore if Elisabeth were a lawyer, then Michael is playing a game.
p -> q. forall x: P(x) -> Q(x). r -> P(a). Q(a) -> s. q -> r. Therefore p -> s.