A × B

Cartesian Product

Learn what a Cartesian product is, see it solved, explore all the ways to represent it, then try it yourself.

What is a Cartesian Product?

If two sets A and B are non-empty sets, then the set of all ordered pairs formed by taking the first element from the set A and the second element from the set B is called the Cartesian product of A and B.

A × B = { ( x , y ) }
x ∈ A y ∈ B
Example 1 of 5
Question 1 of 10
Note: To find A × B, take every element of A and pair it with every element of B.

You solved all questions! 🎉

Let A = {1, 2} and B = {3, 4, 5}. The ways of representing A × B are as follows:
Cartesian product A × B = {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5)}
1. Tabulation Method
B
A ×
(,) (,) (,)
(,) (,) (,)
2. Mapping Diagram Method
Fill in the elements of A and B, then click an element of A followed by an element of B to draw an arrow.
A
B
3. Tree Diagram Method
Place the elements of A, then of B, and watch the branches connect automatically. Fill each ordered pair too.
A
B
A × B
(,)
(,)
(,)
(,)
(,)
(,)
4. Graphical Method
From the tree diagram method, A × B = {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5)}
Click on the grid to plot the point (1, 3).

🎉 All four ways of representing A × B are complete!