Question

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

Answer 1

The Cartesian product $A \times B \times C$ consists of all the ordered triples of the form (a,b,c) where a is an airline and both b and c are cities in the United States.

One way to use the set $A \times B \times C$ represents all airlines that fly from the city B to city C of the United States and $A \times B \times C$ would give us information on the connectivity of the cities using the airline.

Now, we show by an example how the Cartesian product would work.

Let A = {a,b}, B = {x,y} and C = {1}.

Now the Cartesian product of A, B and C is defined as:

$A \times B \times C = {a,b} \times [{x,y} \times {1}] \\ = {a,b} \times [{x,1},{y,1}] \\ = {(a,x,1),(a,y,1),(b,x,1),(b,y,1)}$