Roster and Set Builder Form

Another notation known as “set builder form” is also used to represent sets. Instead of mentioning the set of all items, we use a condition in this manner to express sets. For instance, the set of vowels in English Alphabets can be expressed as {x | x represents vowels in english alphabets} is the set builder notation. Let’s discuss the difference between both the methods of representation as follows:

Difference between Roster and Set Builder Form

The key differences in both roster and set builder forms are listed in the following table:

Aspect	Roster Notation	Set Builder Form
Definition	Lists the elements of the set explicitly.	Describes the set using a rule or condition.
Format	Uses braces { } and lists elements separated by commas or semicolons.	Uses {x: “condition for x”}
Example	{1, 2, 3, 4, 5}	{x: x<6, x ∈ N}
Finite or Infinite	Can represent finite and infinite sets.	Primarily used for infinite sets or sets with a large number of elements.
Readability	Easy to read for small sets with a few elements.	More concise for describing sets with a pattern or rule.
Common Use Cases	Suitable for finite sets or sets with a small number of elements.	Used when describing sets with certain properties, e.g., the set of even numbers, prime numbers, etc.
Set Size	May not be practical for very large sets.	Can describe sets of any size, including infinite sets.
Examples of Infinite Sets	{1, 2, 3, . . .}	{x: x >0, x ∈ N}

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Finite Sets

Equal Sets

Example: Convert the following set from set builder notation into roster notation: P = {x | x is a prime number less than 10}.

Solution:

We know that the prime numbers less than 20 are 2, 3, 5, 7.

Therefore, the given set in roster form is {2, 3, 5, 7}.

Roster Form

Roster Form is one of the two representations that any set can have, with the other representation being Set-Builder Form. In Roster form, all the elements of the set are listed in a row inside curly brackets. If the set comprises more than one element, a comma is used in roster notation to indicate the separation of every two elements. Since each element is counted separately, the roster form is also known as Enumeration Notation.

This article explores the concept of Roster form and helps you learn about this method of representing sets in Set Theory. In addition to details about Roster Form, we will also cover notation, provide examples, and discuss various applications of Roster Form.

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