Translate the following inference to logic notation: If Barbara drives a car, then Michael is a politician. If Michael were a politician, then Barbara is driving a car. If Michael were a politician, then it is raining. John is not writing a letter. It is raining if and only if John is writing a letter. Therefore Barbara is not driving a car.
p -> q. q -> p. q -> r. ~s. r <-> s. Therefore ~p.