Translate the following inference to logic notation: For all x, if x were a mechanic, then x is driving a car. Elisabeth is a mechanic. It is not sunny. It is sunny if and only if William is playing a game. Therefore William is not playing a game and Elisabeth is driving a car.
forall x: P(x) -> Q(x). P(a). ~p. p <-> q. Therefore ~q and Q(a).