Course Navigator
Back To Course
Math 102: College Mathematics14 chapters | 108 lessons
As a member, you'll also get unlimited access to over
Kathryn teaches college math. She holds a master's degree in Learning and Technology.
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.
Let's try another example. Here are a couple sets of clothes I brought on my vacation. Let set A = {shorts, skirt, pants}. Let set B = {shirt, swimsuit, sarong, blouse}. I have so many choices of what to wear; I don't know what to decide! Let's use the Cartesian product to show me all of the possible outfits.
I like to pick my bottoms first, so we will do A x B. Let's use distribute set A into set B: shorts distributed to shirt, swimsuit, sarong and blouse; skirt distributed to shirt, swimsuit, sarong and blouse; pants distributed to shirt, swimsuit, sarong and blouse. So the Cartesian product A x B = {(shorts, shirt), (shorts, swimsuit), (shorts, sarong), (shorts, blouse), (skirt, shirt), (skirt, swimsuit), (skirt, sarong), (skirt, blouse), (pants, shirt), (pants, swimsuit), (pants, sarong), (pants, blouse)}.
Wow! Now all I need to decide is which combination to wear! The Cartesian product is a great way to write out all of my options.
To find the Cartesian product, we can use idea of the distribution property. Take all of the elements in the first set multiplied with every element in the second set.
To unlock this lesson you must be a Study.com Member.
Create your account
Already a member? Log In
BackDid you know… We have over 49 college courses that prepare you to earn credit by exam that is accepted by over 2,000 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
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.