Set Builder Notation

Define Set-Builder Notation.

Set Builder Notation is a way of representing sets using logical statements. It is composed of a variable, a vertical bar (“|”) symbol, and a logical statement outlining the requirements that each member of the set must meet. The set of even numbers, for instance, may be expressed as,

{x | x is an even number}

What’s the Difference between Roster Forms and Set Builder Forms?

In mathematics, there are two ways to express sets:

Roster Form

Set-Builder Form

The roster form lists each component of a set between curly braces and commas. For instance, {1, 2, 3} The elements of the set are described by a rule or condition in the set-builder form. Consider the following example: {x | x is a positive integer less than 4} Set-builder form provides a clear, rule-based specification, whereas the roster form offers an explicit list.

What are Examples of Set Builder Notation?

We represent sets using the Set Builder Notation and some examples of sets represented using the set builder notation are,

{x | x are even numbers less than 24}

{x | x is an integer greater than -2 and less than 4}

{x | x is a fraction where denominator is always greater than numerator}, etc.

How is Domain written in Set Builder Notation?

In set builder notation, the domain of f(x) = 1/x may be written as {x ∈ ℝ | x ≠ 0}. We can state a function’s domain as “all real numbers” if its domain is exclusively made up of real numbers. The range (-∞, ∞) can be used to represent all real numbers.

What are Real Numbers?

Rational and Irrational Numbers are combined to form a group called Real Numbers. It is represented by 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