How to Write a Set Builder Notation?

Let’s go on to the next idea, writing the set-builder notation, now that we understand what that is.

To write sets in set builder notation, follow the instructions below:

  • Use a lowercase letter, such as x, or any other letter, to denote the components of a set.
  • As a divider, use a colon (:) or vertical bar (|).
  • Declare the property’s requirement that every member of the supplied set has items after the symbol.
  • Inside the curly braces{}, type the whole description.

Think about the following illustration where set A is described as:

A = { x ∈ R | x<4 }

Where the symbol means “member of.” The abbreviation “R” stands for “real numbers.” Because x in R can be any number less than 4, set A holds the value of x in R.

Set-Builder Notation

Set-builder Notation is a type of mathematical notation used to describe sets by naming their components or highlighting the requirements that each member of the set must meet. Sets are written in the form of {y | (properties of y)}  OR {y : (properties of y)} in the set-builder notation, where the condition that fully characterizes each member of the collection replaces the attributes of y.

The elements and properties are separated using the character ‘|’ or ‘:’ The entire set is interpreted as “the set of all elements y” such that (properties of y), while the symbols ‘|’ or ‘:’ are read as “such that.”

This article explores the set-builder notation, symbols used in set-builder notation, examples, representation of sets methods, etc.

Table of Content

  • What is Set-Builder Notation?
  • Symbols Used in Set Builder Notation
  • Representation of Sets Methods
  • Tabular or Roster Form
  • Examples of Roster Method
  • Set-Builder Notation
  • Why Do We Use Set Builder Form?
  • How to use a Set Builder Notation?
  • How to Write a Set Builder Notation?
  • How to read Set Builder Notation?
  • Set Builder Notation for Domain and Range
  • Set Builder Notation Examples

Similar Reads

What is Set-Builder Notation?

A representation or notation known as “set-builder notation” is used to express a set that is defined by a logical formula that simplifies to be true for each element of the set. There may be one or more variables included. It also specifies a rule for the set’s constituent members....

Symbols Used in Set Builder Notation

The elements of the set are represented by a variety of symbols in the set builder form. Here is a list of some of the symbols....

Representation of Sets Methods

There are two different methods to represent sets. These are:...

Tabular or Roster Form

The items of the set are enumerated using the roasting method’s braces{}, with commas between each piece. The element can only be written once if it appears more than once in the collection....

Examples of Roster Method

The formula for the first five natural integers, designated as set X, is X = {6, 7, 8, 9} The letter combinations {D, L, H, I} make up the set A of the word DELHI....

Set-Builder Notation

If a set’s components share a property, that property can be used to define the components. For instance, the set A = {1, 2, 3, 4, 5, 6} has a trait in common that all of its members are natural integers lower than 7. Other natural numbers do not have this characteristic. As a result, the set X may be expressed as follows:...

Why Do We Use Set Builder Form?

When there are many components and utilizing the roster form makes it difficult to represent the components of the set, set builder notation is employed. Let’s use an illustration to better grasp this. If you need to write a list of numbers from 1 to 8 inclusively, you may just write {1, 2, 3, 4, 5, 6, 7, 8} using the roster notation....

How to use a Set Builder Notation?

A mathematical notation known as “set builder notation” lists all the requirements that each member of a set must meet in order to be included in the set. In particular, it helps to understand sets with an unlimited number of items....

How to Write a Set Builder Notation?

Let’s go on to the next idea, writing the set-builder notation, now that we understand what that is....

How to read Set Builder Notation?

A technique for expressing set attributes that hold true for each and every element contained in the set is called set builder notation. The format of set builder notation is as follows:...

Set Builder Notation for Domain and Range

Writing the domain and range of a function using the set builder notation is quite helpful. The set of all the values that are input into a function is the domain of the function. For example, the domain of the rational function f(x) = 2/(x-1) would include all real integers other than 1. This is due to the fact that when x = 1, the function f(x) would be undefined. As a result, the domain of this function is written as  {x ∈ R | x ≠ 1}....

Set Builder Notation Examples

Example 1: Use the set-builder notation to represent the given set....

Summary – Set-Builder Notation

Set-builder notation is a mathematical shorthand used to define sets based on specific properties that all elements of the set share. It is particularly useful when dealing with large or complex sets where listing all elements individually would be impractical or impossible. In set-builder notation, you typically start with a variable that represents the elements of the set, followed by a vertical bar (|) or colon (:), which can be read as “such that.” After this separator, you describe the condition or rule that all elements must satisfy to be included in the set....

Set Builder Notation – FAQs

Define Set-Builder Notation....

Contact Us