A town has a road network that consists entirely of one-way streets that are used for bus routes. Along these routes, bus stops have been set up. If the one-way signs permit travel from bus stop X to bus stop Y=X, then we shall say Y can be reached from X. We shall use the phrase Y comes after X when we wish to express that every bus stop from which the bus stop X can be reached is a bus stop from which the bus stop Y can be reached, and every bus stop that can be reached from Y can also be reached from X. A visitor to this town discovers that if X and Y are any two different bus stops, then the two sentences “Y can be reached from X” and “Y comes after X” have exactly the same meaning in this town. Let A and B be two bus stops. Show that of the following two statements, exactly one is true:
(i) B can be reached from A;
(ii) A can be reached from B. combinatorics proposedcombinatorics