Education Portal is now Study.com! Same great content, just under a new name. Learn more
Copyright

How to find the Cartesian Product

  • 0:05 A Cartesian Product Vacation
  • 2:23 Example
  • 3:41 Lesson Summary
Create An Account
To Start This Course Today
Used by over 10 million students worldwide
Create An Account
Try it free for 5 days
Lesson Transcript
Instructor: Kathryn Maloney

Kathryn teaches college math. She holds a master's degree in Learning and Technology.

The Cartesian product allows us to take two sets of mathematical objects and create one new one. With one simple idea, the Cartesian product becomes quick and easy.

A Cartesian Product Vacation

Let's say we have two sets of free meals available on my vacation. Set A = {coffee, tea, milk}. These are my choices of free beverages. Set B = {breakfast, lunch}. These are the free meals with my vacation.

The Cartesian product, written A x B, is putting the elements from set A and elements in set B together. So the Cartesian product A x B = {(coffee, breakfast), (coffee, lunch), (tea, breakfast), (tea, lunch), (milk, breakfast), (milk, lunch)}. The Cartesian product is always written like an ordered pair: (first element, second element).

So I can have coffee with breakfast or lunch, tea with breakfast or lunch, or milk with breakfast or lunch. It is like you distribute set A into set B: coffee distributed to breakfast and lunch, tea distributed to breakfast and lunch, milk distributed to breakfast and lunch. It would give us our answer A x B = {(coffee, breakfast), (coffee, lunch), (tea, breakfast), (tea, lunch), (milk, breakfast), (milk, lunch)}.

If I have the Cartesian product B x A, we would have B x A = {(breakfast, coffee), (breakfast, tea), (breakfast, milk), (lunch, coffee), (lunch, tea), (lunch, milk)}. In this case, I can have breakfast with coffee, breakfast with tea, or breakfast with milk. I can also have lunch with coffee, lunch with tea, or lunch with milk. It is like you distribute set B into set A: breakfast distributed to coffee, tea, and milk; lunch distributed to coffee, tea, and milk. It would give us our answer B x A = {(breakfast, coffee), (breakfast, tea), (breakfast, milk), (lunch, coffee), (lunch, tea), (lunch, milk)}. This is the Cartesian product.

To unlock this lesson you must be a Study.com Member.
Create your account

Unlock Your Education

See for yourself why 10 million people use Study.com

Become a Study.com member and start learning now.
Become a Member

Already a member? Log In

Start Your Free Trial To Take This Quiz

As a member, you'll also get unlimited access to over 10,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
It only takes a few minutes to set up and you can cancel at any time.
Already registered? Login here for access

Practice Final Exam


Practice Chapter Exam

Earning College Credit

Did you know… We have over 100 college courses that prepare you to earn credit by exam that is accepted by over 2,900 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.