We note that the basic form of a complicated truth function is A => B. Thus determining validity of the corresponding argument reduces to inspecting whether it is possible for such an implication to be false ie whether it is possible for A to be true and B to be false. We consider what happens if we assume that this is the case. In doing so, we will either hit a contradiction which will assure us that it cannot happen in the first place, or else we will find values that demonstrate it can indeed be false.