# Venn Diagrams: Subset, Disjoint, Overlap, Intersection & Union

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Categorical Propositions: Subject, Predicate, Equivalent & Infinite Sets

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

Replay
Your next lesson will play in 10 seconds
• 0:05 Set Review
• 1:30 Set Operations
• 2:42 Venn Diagram
• 5:15 Lesson Summary
Add to Add to

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

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.

The Venn diagram was introduced by John Venn. Yes, the Venn diagram is named after a real person! His idea was to show sets in terms of pictures. The Venn diagram is now used in many fields, including mathematics. Let's take a look at John Venn's idea.

## Set Review

Before we get into Venn diagrams, let's review sets. A set is a collection of elements. An element is a collection of anything - numbers, letters, words, objects. Using math symbols, the symbol below means element.

A subset is a special, funny set. If every element in one set is included in another set, they are called subsets. Using math symbols, the symbol below means subset.

Let's say our universe is the things, or elements, in my apartment. So, our universal set U = {fork, spoon, knife, spatula, whisk, plate, cup, napkin, tablecloth, television, couch}.

Let set K be a list of utensils in my kitchen. K = {fork, spoon, knife, spatula, whisk}.

Let set T be a list of things, or elements, on my table. T = {plate, fork, knife, cup, napkin, tablecloth}.

So, we can say that a fork is an element of K. Using math symbols, we would write:

This is read, 'Fork is an element of K,' or, 'Fork belongs to K.' That makes sense because the fork belongs in the kitchen.

## Set Operations

Let's use sets K and T to review set operations.

### Union

Union is when two or more sets are united, or added together.

K union T = all of the elements of set K or all of the elements in set T, and that would equal {fork, spoon, knife, spatula, whisk, plate, cup, napkin, tablecloth}.

The 'or' tells us that it is any object in set K, the kitchen, or set T, on the table.

### Intersection

Intersection is when two or more sets intersect, or are common objects, in sets.

K intersects T = all of the numbers in set K and set T, and that equals {fork, knife}.

The 'and' tells us that it is in the kitchen and on the table at the same time.

### Complement

Complement is when a set is subtracted or not included in the set.

K' = everything not in the kitchen, not in set K, and that equals {plate, cup, napkin, tablecloth, television, couch}.

## Venn Diagram

A Venn diagram can show us the sets and operations nicely in picture form. Let's look at union, intersection and complement using a Venn diagram. We're going to continue using set K and set T. Below is what a Venn diagram showing the sets K and T looks like:

Let's examine how the Venn diagram is created.

There's a circle for each set - one circle for set K and another circle for set T. You can see that we labeled the circles so we don't get them mixed up. We only have two circles because we only have two sets, but you will also see Venn diagrams with more than two circles.

The circles intersect because there are objects, or elements, in each set that are the same. We would say K intersects T = {fork, knife}.

I hope you notice that television and couch are listed in the universal set, but not found in set K or set T. Even though we didn't use it in a set, we still need to show it. In all cases where this happens, we list it outside the circles but within the box or universe.

#### Union

K union T = {fork, spoon, knife, spatula, whisk, plate, cup, napkin, tablecloth}.

To show union in a Venn diagram, we highlight the circle K and circle T:

#### Intersection

K intersects T = {fork, knife}.

To show intersection in a Venn diagram, we highlight only where the two circles intersect each other in the middle of our picture:

#### Complement

K' = {plate, cup, napkin, tablecloth, television, couch}.

To show complement in a Venn diagram, we highlight everything except the circle that represents set K:

#### Subset

Let's pretend we have another set called B = {spatula, whisk}, elements we would need to bake. That means in our Venn diagram we need another circle inside of K.

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

### 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 95 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

### 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!

Support