Translate the following inference to logic notation: For all x, x will play a game if and only if x is a police officer. William is not a scientist. If it rains, then William is a scientist. If Thomas plays a game, then it is raining. Therefore Thomas is not a police officer or it is overcast.
forall x: P(x) <-> Q(x). ~p. q -> p. P(a) -> q. Therefore ~Q(a) or r.