# Ch 10: Sets & Relations in Math

### About This Chapter

## Sets & Relations in Math - Chapter Summary

Your understanding of sets and relations in math can skyrocket by taking advantage of the entertaining lessons in this chapter. Expert instructors make it easy to comprehend ordered pairs, equivalent sets, mathematical sets, Venn diagrams, the two-way table and much more. Review these lessons whenever it's most convenient to ensure you're able to:

- Understand groups and sets in algebra
- Write sets using set builder notation
- Differentiate between relations and functions
- Define equivalence relation and the union of sets in math
- Share the meaning of cardinality and list types of subsets
- Find the Cartesian product

Enjoy the ability to access all the resources in this chapter in a secure online environment. Whether studying from home or on-the-go, you can view the lessons and take the multiple-choice quizzes using your computer, smartphone or tablet. Navigate the lessons in your sequence of choice, and use mini quizzes and a practice exam to test your understanding. If you develop questions while reviewing this chapter, feel free to send them to our experts.

### 1. Introduction to Groups and Sets in Algebra

As an introduction to the algebraic concepts of sets and groups, this lesson covers the difference between the two concepts and how to determine if a set is a group. To complete this lesson, we'll take a look at some practice examples.

### 2. How to Write Sets Using Set Builder Notation

Set builder notation allows the user to indicate specific items that are to be included within a set. In this lesson, we will learn how to write sets using set builder notation.

### 3. Ordered Pair: Definition & Examples

An ordered pair is a simple way of keeping track of two numbers by writing them in a specific order. Learn about ordered pairs and how they are useful.

### 4. Relation in Math: Definition & Examples

In this lesson, you will learn the definition of relation in terms of mathematics, as well as the various ways of displaying relations. We will also look at some examples.

### 5. The Difference Between Relations & Functions

Relations and functions are a huge part of mathematics. In this lesson, we will define relations and functions. We will look at the differences between the two and how to determine whether a given relation is a function.

### 6. Equivalent Sets: Definition & Example

In this lesson, you'll learn the definition of equivalent sets. We'll look at some properties and terms related to equivalent sets, as well as examples so you can gain a better understanding of this concept.

### 7. Equivalence Relation: Definition & Examples

How can we relate two things? Is there a formal way to say that two things are equivalent, while also saying that two things are not equivalent? Equivalence relations can do that!

### 8. Union of Sets in Math: Definition, Terms & Symbol

In this lesson, learn about how you use sets and their unions in everyday life. Learn how to appropriately write them so that you can communicate with others about sets. Also, learn how easy they are to use.

### 9. Mathematical Sets: Elements, Intersections & Unions

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.

### 10. Cardinality & Types of Subsets (Infinite, Finite, Equal, Empty)

In this video, we will add to our knowledge of sets. We will talk about cardinality, infinite, finite, equal and the empty set. I think you will find these very straightforward, so let's begin.

### 11. How to Find the Cartesian Product

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.

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

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.

### 13. What is a Two-Way Table?

Do you believe in Martians? Do you watch football on television? A Two-Way Table or Contingency Table is a great way to show the results of all kinds of survey questions. In this video we will learn how to read a two-way table.

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### Other Chapters

Other chapters within the BITSAT Exam - Math: Study Guide & Test Prep course

- Expressions & Reasoning in Math
- Complex Numbers & Polynomials in Algebra
- Introduction to Quadratics
- Working with Quadratic Functions Overview
- Mathematical Sequences & Series Overview
- Series & Sequences Application
- Exponential Functions & Logarithmic Equations
- Binomial Theorem Overview
- Overview of Matrices & Determinants
- Introduction to Trigonometric Functions
- Trigonometric Identities Overview
- Real World Trigonometric Applications
- Operating with Functions
- Solving Inequalities
- Two-Dimensional Coordinate Geometry
- Straight Lines & Angles in Coordinate Geometry
- Circular Arc & Circles in Coordinate Geometry
- Conic Sections in Coordinate Geometry
- Three-Dimensional Coordinate Geometry
- Limits & Continuity in Differential Calculus
- Calculating Derivatives
- Differentiable Functions & Min-Max Problems
- Differentiability in Integral Calculus
- Overview of Probability in Calculus
- Vectors & Scalars in Math
- Dispersion & Frequency Distributions in Statistics
- Linear Programming & Systems of Equations
- Definite Integrals
- Permutation & Combination
- Mathematical Modeling Overview
- BITSAT Exam - Math Flashcards