Back To Course

Supplemental Math: Study Aid1 chapters | 19 lessons

Watch short & fun videos
**
Start Your Free Trial Today
**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 70,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*David Liano*

After completing this lesson, you will be able to define universal set and write examples of universal sets. You will also be able to utilize universal sets to create subsets of universal sets.

A universal set does not have to be the set of everything that is known or thought to exist - such as the planets, extraterrestrial life and the galaxies - even though that would be one example of a universal set. A **universal set** is all the elements, or members, of any group under consideration.

For instance, all the stars of the Milky Way galaxy could be a universal set if we are discussing all the stars of the Milky Way galaxy. This type of universal set might be appropriate for astronomers, but it is still a pretty large set of objects to consider.

A typical universal set in mathematics is the set of natural numbers as shown below: **N** = {1, 2, 3, 4, ...}.

Boldface capital letters are sometimes used to identify certain number sets, such as **N** for natural numbers. We usually use braces to enclose a set. The ellipsis mark (...) tells us that the set of natural numbers goes on without end; so this universal set is also an infinite set. However, universal sets can also be finite sets.

Let's look at an example of a universal set that is finite. The set of all the presidents of the United States is an example of a universal set that is finite. This set may increase every four years, but at any given time, it is a finite universal set if we are discussing all the men who have been president of the United States.

Sets are usually named with a capital letter. Therefore, the universal set is usually named with the capital letter **U**. This will be the notation used in this lesson.

Sometimes, alternate notation might be used for a universal set, such as the example of the set of natural numbers shown above. The set of natural numbers is not necessarily a universal set. Whether a set is a universal set is based on the structure of a problem or on the situation under examination. But the point here is that alternate notation can be used to name a universal set as long as it is practical and clear to the observer.

If all the elements of set **A** are also elements of set **B**, then **A** is a **subset** of **B**. This means that subsets can be created from any defined universal set. We should first acknowledge that any universal set is a subset of itself. However, a subset usually has less elements than the universal set from which it is created.

Let's go back to the set of natural numbers. Suppose we wanted to list all the natural numbers that satisfy the equation 20 < *x* < 25. This subset is shown next: {21, 22, 23, 24}.

The set of natural numbers itself is a subset of the set of real numbers, which could be another example of a universal set. Again, what is or isn't a universal set is based on the context of a problem.

Let's next go back to the universal set we created for the presidents of the United States: **U** = the set of the presidents of the United States. We want to create a subset from **U**.

We will create a subset of all the presidents of the United States who died in office. Let's call this set **A**, which is defined next: **A** = {Harrison, Taylor, Lincoln, Garfield, McKinley, Harding, F. Roosevelt, Kennedy}.

The inside of the rectangular shape represents the universal set. In other words, all the elements, or members, of **U** are represented by the area inside the rectangle. The subset **A** is represented by the circle. Of course, the total area of the circle needs to be inside the area of the rectangle.

Let's show one more example of a universal set and a subset of a universal set using a topic in mathematics. This will give us a chance to show additional notation used in sets. Our universal set will be all positive odd numbers less than 100: **U** = {1, 3, 5, 7, ... 99}.

The above notation shows that the pattern of consecutive positive odd numbers will continue to the number 99. Our subset will be all the prime numbers that are elements of this universal set, and we will call it set **B**: **B** = {3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}.

This notation can be read as the set of all numbers *x* that are elements of the universal set, such that *x* is a prime number. The curvy E-symbol states that *x* is an element of **U**, and the vertical line (|) is understood to mean 'such that.'

A **universal set** is the set of all elements, or members, of a group under consideration. This group is usually relevant to a particular situation, such as a mathematical problem or some point of discussion. The creation of universal sets is handy when discussing a specific issue that pertains to only a certain set of members, such as the senior class of a high school. Finally, additional sets, called subsets, can be created from a universal set.

By the end of this lesson you should be able to define, interpret, and create a universal set and a related subset.

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 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

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.

You are viewing lesson
Lesson
6 in chapter 1 of the course:

Back To Course

Supplemental Math: Study Aid1 chapters | 19 lessons

- Less Than Symbol in Math: Problems & Applications 4:10
- What are 2D Shapes? - Definition & Examples 4:35
- Trapezoid: Definition, Properties & Formulas 3:58
- What is Surface Area? - Definition & Formulas 5:56
- Using Parentheses in Math: Rules & Examples 3:58
- Universal Set in Math: Definition, Example & Symbol 6:03
- Zero Exponent: Rule, Definition & Examples 4:32
- Quotient Of Powers: Property & Examples 4:58
- What is Simplest Form? - Definition & How to Write Fractions in Simplest Form 5:49
- What is Slope? - Definition & Formulas 7:10
- Skewed Distribution: Examples & Definition 5:09
- Change Of Base Formula: Logarithms & Proof 4:54
- Transformations in Math: Definition & Graph 6:27
- What is Translation in Math? - Definition, Examples, & Terms 4:23
- Fixed Interval: Examples & Definition 4:00
- Scatterplot and Correlation: Definition, Example & Analysis 7:48
- Dilation in Math: Definition & Meaning 5:30
- Simplifying Fractions: Examples & Explanation 4:44
- Go to Overview of Math Concepts

- NES Social Science: Help & Review
- Computer Science 311: Artificial Intelligence
- View High School: English 4
- View High School: English 3
- View High School: English 2
- Major Political Developments from 1350-1871
- The 1920s in the U.S.
- The Legacy of Ancient Greece & Rome
- Sectionalism & the American Civil War
- Causes & Consequences of the Cold War
- FTCE Prep Product Comparison
- TExES Prep Product Comparison
- Study.com ASVAB Scholarship: Application Form & Information
- Study.com GED Scholarship: Application Form & Information
- Study.com GACE Scholarship: Application Form & Information
- Study.com CSET/CBEST Scholarship: Application Form & Information
- Study.com NES Scholarship: Application Form & Information

- U.S. Healthcare Safety Net Services: Types & Trends
- Integrated Marketing Communication Metrics
- Trajectory Theory: Definition & Examples
- Incentives in Negotiation: Use & Importance
- Using Reason & Emotion to Create & Sustain Change in Organizations
- Evaluating ELD Programs: Discourse Competence
- How to Identify & Prevent Potential Problems in Team Settings
- LGBTQ Issues & Representation in Theatre
- Quiz & Worksheet - Recording Post-Retirement Benefit Expenses
- Quiz & Worksheet - Types of Bond Risk
- Quiz & Worksheet - Cognitive Reference Points
- Quiz & Worksheet - Alice Munro's Life & Sayings
- Quiz & Worksheet - How to Teach Decimal Operations
- International Law & Global Issues Flashcards
- Foreign Policy, Defense Policy & Government Flashcards

- Business Math Textbook
- TExES Physics/Mathematics 7-12 (243): Practice & Study Guide
- Critical Thinking Study Guide
- Human Resource Management for Teachers: Professional Development
- FTCE General Knowledge Test (GK) (827): Reading Subtest Practice & Study Guide
- History of Our World Chapter 6: The Rise of Ancient Greece
- GRE Psychology: History & Development of Modern Psychology
- Quiz & Worksheet - Restorative Justice Protocol
- Quiz & Worksheet - The Bosnian Genocide
- Quiz & Worksheet - Secondary Prevention in Healthcare
- Quiz & Worksheet - Sex Offenders Types, Laws & Rights
- Quiz & Worksheet - Primary Sources for Writing

- School Violence Prevention: Programs & Strategies
- What is Paleobotany? - Definition & Importance
- Do Homeschoolers Have to take Standardized Tests?
- West Virginia Homeschool Laws
- NBCOT Renewal Requirements
- Best MCAT Prep Books
- Average MCAT Scores
- Do Private Schools Take Standardized Tests?
- Books Every English Major Should Read
- How To Get a Copy of Your High School Diploma
- Special Education Laws in Florida
- Homeschooling in Delaware

Browse by subject