Like?

# How to find the Cartesian Product

Start Your Free Trial To Continue Watching
As a member, you'll also get unlimited access to over 8,500 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 minute. You can cancel at any time.
Start your free trial to take this quiz
As a premium member, you can take this quiz and also access over 8,500 fun and engaging lessons in math, English, science, history, and more. Get access today with a FREE trial!
Free 5-day trial
It only takes a minute to get started. You can cancel at any time.
1. 0:05 A Cartesian Product Vacation
2. 2:23 Example
3. 3:41 Lesson Summary
Share
Show Timeline

### 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.

## Unlock Content Over 8,500 lessons in all major subjects

Get FREE access for 5 days,
just create an account.

No obligation, cancel anytime.

Select a subject to preview related courses:

###### People are saying…

"This just saved me about \$2,000 and 1 year of my life." — Student

"I learned in 20 minutes what it took 3 months to learn in class." — Student

See more testimonials

Yes No

### What didn't you like?

What didn't you like?