Translate the following inference to logic notation: If it is late, then Barbara is a police officer. David is listening to a song. If it is overcast, then Barbara is a police officer. If it is overcast, then David is not listening to a song. If Barbara were a police officer, then it is overcast. Therefore it is not late.
p -> q. r. s -> q. s -> ~r. q -> s. Therefore ~p.