# Mathematical Sets: Elements, Intersections & Unions

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

### You're on a roll. Keep up the good work!

Replay
Your next lesson will play in 10 seconds
• 0:10 Understanding Sets
• 0:55 Unions
• 1:37 Intersections
• 2:18 Lesson Summary
Timeline
Autoplay
Autoplay
Create an account to start this course today
Try it free for 5 days!

#### Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Kathryn Maloney

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

Today we're going to explore mathematical sets, which are surprisingly simple! Sets are just collections of any objects or concepts, also known as elements, that can be related to each other through union or intersection.

## Understanding Sets

A set is a collection of objects, and it doesn't need to be a number!

This is the set of the clothes in my closet: C = {pants, t-shirt, skirt, and dress}. The capital C represents the set. So, if I said set C, we know I'm talking about clothes in my closet. The braces, { }, denote the elements, or members of the set. The elements of set C are pants, t-shirt, skirt, and dress.

You're probably familiar with a set of real numbers: R = {â€¦-3, -2, -1, 0, 1, 2, 3...}. The three dots indicate that the pattern continues. The elements of this group are all real numbers. So, R equals the set of real numbers.

## Unions

To collect sets together, we use the term union. We unite the sets into one.

Let's say I have two sets. Set A is green, blue, and pink. Set B is orange, yellow, and black. A u B represents the union of sets A and B. Yes, that u symbol represents union! It's kind of handy! A u B represents all the elements that are listed in set A, or in set B, or in both. How would that look in using mathematical symbols? A u B = {green, blue, pink, orange, yellow, black}.

## Intersections

To find elements in common with sets, we use the term intersection. Think of the sets as two roads that meet at an intersection. What do the two roads, or sets, have in common?

Let's say I have two sets. Set A is 4, 6, and 9. Set B is 7, 8, and 9. A intersect B represents the intersection of sets A and B. Yes, that upside down u represents intersection! This represents all the elements that are the same in A and B. How would that look in using mathematical symbols? A intersect B = {9}.

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

### Register for a free trial

Are you a student or a teacher?
What is your educational goal?
Back

Back

### Earning College Credit

Did 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.

### 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.

Create an account to start this course today
Try it free for 5 days!

#### Explore our library of over 30,000 lessons

Click "next lesson" whenever you finish a lesson and quiz.
You now have full access to our lessons and courses. Watch the lesson now or keep exploring.
You're 25% of the way through this course! Keep going at this rate,and you'll be done before you know it.
1
The first step is always the hardest! Congrats on finishing your first lesson.
5
Way to go! If you watch at least 30 minutes of lessons each day you'll master your goals before you know it.
10
Congratulations on earning a badge for watching 10 videos but you've only scratched the surface. Keep it up!
20
You've just watched 20 videos and earned a badge for your accomplishment!
50
You've just earned a badge for watching 50 different lessons. Keep it up, you're making great progress!
100
You just watched your 100th video lesson. You have earned a badge for this achievement!
200
Congratulations! You just finished watching your 200th lesson and earned a badge!
300
Congratulations! You just finished watching your 300th lesson and earned a badge!
500
You are a superstar! You have earned the prestigious 500 video lessons watched badge.
1K
Incredible. You have just entered the exclusive club and earned the 1000 videos watched badge.
20
You have earned a badge for watching 20 minutes of lessons.
50
You have earned a badge for watching 50 minutes of lessons.
100
You have earned a badge for watching 100 minutes of lessons.
250
You have earned a badge for watching 250 minutes of lessons.
500
You have earned a badge for watching 500 minutes of lessons.
1K
You have earned a badge for watching 1000 minutes of lessons.
Support