Math Lesson 16.1.2 - Cartesian Product

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Welcome to our Math lesson on Cartesian Product, this is the second lesson of our suite of math lessons covering the topic of Relation and Function, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Cartesian Product

Let us consider two number sets A = {1, 2, 3} and B = {12, 15}. Let's suppose we have a task to form all possible ordered pairs with the elements of these two sets. As stated above, the first element of each pair must belong to set A while the second element to set B. Given this condition, we obtain the following list of ordered pairs:

By definition, the set composed of all these ordered pairs is called the Cartesian product of the two sets A and B. In symbols, we represent the Cartesian product as A × B.

An example of the application of the Cartesian product in practice is the coordinates system, otherwise known as the Cartesian plane, where all ordered pairs represent a specific point of the coordinates system.

Example 2

The number sets

1. Find all elements of
   A × B
2. Show the ordered pairs found in (a) in the Cartesian plane

Solution 2

1. The elements of
   A × B
   are all ordered pairs obtained by the combination of all elements of the two sets A and B. Thus, we have
   A × B = {(2, 4), (2, 6), (3, 4), (3, 6), (5, 4), (5, 6)}
2. All the ordered pairs above represent a specific point in the coordinates system, where the set A represents the X-axis while the set B the Y-axis. They are shown in the graph below.

You have reached the end of Math lesson 16.1.2 Cartesian Product. There are 9 lessons in this physics tutorial covering Relation and Function, you can access all the lessons from this tutorial below.

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