What is the Cartesian product A × B × C, where A is the set of all airlines and

Question

What is the Cartesian product A × B × C, where A is the set of all airlines and B and C are both the set of all cities in the United States? Give an example of how this Cartesian product can be used. What is the Cartesian product A × B × C, where A is the set of all airlines and B and C are both the set of all cities in the United States? Give an example of how this Cartesian product can be used. What is the Cartesian product A × B × C, where A is the set of all airlines and B and C are both the set of all cities in the United States? Give an example of how this Cartesian product can be used.

Explanation / Answer

. The elements of A × B × C consist of 3-tuples (a, b, c), where a A, b B, and c C, whereas the elements of (A × B) × C look like ((a, b), c)—ordered pairs, the first coordinate of which is again an ordered pair

. The set of triples (a, b, c), where a is an airline and b and c are cities. A useful subset of this set is the set of triples (a, b, c) for which a flies between b and c.

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