Computer Science: Discrete Mathematics.

Package delivery company is getting ready for the holiday rush. Presently, the company covers several cities, as shown by the routes below. Troy to Funroe Troy to Neverland Neverland to Funroe Mayberry to Funroe Mayberry to Neverland Neverland to Troy Athens to Mayberry

For various reasons, these routes travel in the stated direction only. Also, assume it is always possible to deliver a package within a city (in other words, the adjacency relation is reflexive). Each year, it seems that last-minute shoppers want to ship a package from one town to another, but there is no possible route to accomplish the delivery. The company has hired you to analyze the delivery routes and produce all possible paths, to help the company decide whether they should add additional routes.

We can solve the problem by modeling it as a directed graph. Is the adjacency relation transitive? If not, show two of the ordered pairs that would need to be added to make the relation transitive.

Construct the corresponding adjacency matrix:

	Athens	Funroe	Mayberry	Neverland	Troy
Athens
Funroe
Mayberry
Neverland
Troy

After the first iteration of Warshall's algorithm, the reachability matrix looks as follows:

	Athens	Funroe	Mayberry	Neverland	Troy
Athens
Funroe
Mayberry
Neverland
Troy

After the second iteration of Warshall's algorithm, the reachability matrix looks as follows:

	Athens	Funroe	Mayberry	Neverland	Troy
Athens
Funroe
Mayberry
Neverland
Troy

After the third iteration of Warshall's algorithm, the reachability matrix looks as follows:

	Athens	Funroe	Mayberry	Neverland	Troy
Athens
Funroe
Mayberry
Neverland
Troy

After the fourth iteration of Warshall's algorithm, the reachability matrix looks as follows:

	Athens	Funroe	Mayberry	Neverland	Troy
Athens
Funroe
Mayberry
Neverland
Troy

After the fifth iteration of Warshall's algorithm, the reachability matrix looks as follows:

	Athens	Funroe	Mayberry	Neverland	Troy
Athens
Funroe
Mayberry
Neverland
Troy

Based on the contents of the final reachability matrix, for each city, list the cities to which a package delivery is/is not possible: 1 - From Athens, it (is/is not ) possible to deliver to Funroe it (is/is not ) possible to deliver to Mayberry it (is/is not ) possible to deliver to Neverland it (is/is not ) possible to deliver to Troy

2 - From Funroe, it (is/is not ) possible to deliver to Athens it (is/is not ) possible to deliver to Mayberry it (is/is not ) possible to deliver to Neverland it (is/is not) possible to deliver to Troy

3 - From Mayberry, it (is/is not ) possible to deliver to Athens it (is/is not ) possible to deliver to Funroe it (is/is not ) possible to deliver to Neverland it (is/is not ) possible to deliver to Troy

4 - From Neverland, it (is/is not ) possible to deliver to Athens it (is/is not ) possible to deliver to Funroe it (is/is not ) possible to deliver to Mayberry it (is/is not ) possible to deliver to Troy

5 - From Troy, it (is/is not ) possible to deliver to Athens it (is/is not ) possible to deliver to Funroe it (is/is not ) possible to deliver to Mayberry it (is/is not ) possible to deliver to Neverland