Roster Form

The roster notation of a set is a simple representation of the set in mathematical form. In the roster form, the elements (or members) of a set are listed in a row inside the curly brackets. Every two elements are separated by a comma symbol in a roster notation if the set contains more than one element. The roster form is also called the enumeration notation as the enumeration is done one after one.

In this article, we will learn about the roster form of a set by understanding the use of roster notation, the different types of numbers used in roster form, and how to apply them while solving problems. We will also discover interesting facts about them.

1.	What is Roster Notation?
2.	Roster Form from Venn Diagram
3.	Limitations of Roster Notation
4.	Roster Form and Set Builder Form
5.	FAQs on Roster Form

What is Roster Form?

The roster form is a way of representing sets where the elements of a set are represented in a row surrounded by curly brackets and if the set contains more than one element then every two elements are separated by commas. For example, if A is the set of the first 9 natural numbers, it can be represented by: A = {1, 2, 3, 4, 5, 6, 7, 8, 9}

☛Note:

The elements in roster form can be in any order (they don't need to be in ascending/descending order).
The elements should not be repeated in set roster notation.

Roster Notation

A method of listing the elements of a set in a row with comma separation within curly brackets is called roster notation. An example of the roster form of a set is given below:

Roster Form is followed by a set with natural numbers listed from 1 to 9.

Roster Form from Venn Diagram

Roster form is one of the most simple techniques to represent the elements of a set. The elements can be represented in a row and are easy to read and understand. For example, the set of the first 20 natural numbers divisible by 5 can be represented in roster notation like A = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100}.

Given below are 3 Venn diagrams representing three different sets. Let us represent them in roster form step-wise.

Roster Form from Venn diagram has 3 Venn diagrams representing 3 sets

Set A contains only a single element hence the elements in roster form can be represented with curly brackets ⇒ A = {10}.
Set B contains multiple elements hence the elements can be represented in roster form as B = {3, 7, 4, 5, 8, 11}
The elements of set C can be represented in roster form as C = {x, y, z}

Limitations of Roster Notation

One of the limitations of roster notation is that we cannot represent a large number of data in roster form. For example, if we want to represent the first 100 or 200 natural numbers in a set B then it is hard for us to represent this much data in a single row. This limitation can be overcome by representing data with the help of a dotted line. Take a set of the first 100 positive odd numbers and represent them using roster notation.

B = {1, 3, 5, 7, ....., 199}

The dotted line shows that the numbers are part of set B but not written in set roster notation. When we represent large numbers of elements in a set using roster form we usually write the first few elements and the last element and we separate these elements with a comma. Let's take a set of all the English alphabets, it can be represented in roster form as:

C = {a, b, c, d, ......., z}

If any set has an infinite number of elements like the set of all the even positive integers, it can be represented in roster form like:

D = {2, 4, 6, 8, ......}

We simply can denote the rest of the numbers with a dotted line since there is no end to positive even numbers, we have to keep it like this.

Roster Form and Set Builder Form

There is another notation used to represent sets known as "set builder form". In this form, we represent the sets by using a condition instead of mentioning the set of all elements. For example, the set of alphabets in English, in set builder notation, can be written as {x | x is an alphabet in English}. Here are more differences between the roster form and the set builder form.

Roster Form	Set Builder Form
Provides a list of all elements.	Defines the set by using a logical condition.
Example: {1, 2, 3, 4}	Example: {x ∈ N \| 1 ≤ x ≤ 4}
Suits for sets with a lesser number of elements.	Suits for sets with more elements.
Easy to understand.	Little tricky for non-math people.

Important Notes on Roster Form:

In the roster form, the elements (or members) of a set are listed in a row inside the curly brackets.
The roster form is also called the enumeration form.
The roster form for an empty or null set is represented by ∅.
The roster notation is not used for too much data.

☛Related Topics:

Roster Form Examples

Example 1: Express the below two sets X and Y in the roster form.

Solution: The set X in roster form can be expressed like: X = {1, 2, 3, 4}. The set Y in roster form can be expressed like: Y = {D, B, C, A}

Answer: X = {1, 2, 3, 4}, Y = {D, B, C, A}
Example 2: Express the set A = {x | x = 2n² - 1, where n ∈ N and n < 5} in roster form.

Solution: The elements of set A are:
- For n = 1, 2n²− 1 = 2 × 1² −1 = 1
- For n = 2, 2n²− 1 = 2 × 2²− 1 = 7
- For n = 3, 2n²− 1 = 2 × 3²− 1 = 17
- For n = 4, 2n²− 1 = 2 × 4²− 1 = 31
- For n = 5, 2n²− 1 = 2 × 5²− 1 = 49
Answer: A = {1, 7, 17, 31, 49}
Example 3: Convert the following set from set builder notation into roster notation: P = {x | x is a prime number less than 20}.

Solution:

We know that the prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, and 19.

Therefore, the given set in roster form is {2, 3, 5, 7, 11, 13, 17, 19}.

Answer: {2, 3, 5, 7, 11, 13, 17, 19}

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Practice Questions on Roster Form

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FAQs on Roster Form

What is the Roster Form of Set?

The roster form to represent the set is one of the easiest representations. In roster form, the elements of a set are represented in a row and separated by a comma. For example, the set of first five positive even numbers is represented as A = {2, 4, 6, 8, 10}.

Give an Example of Roster Form.

An example of roster form: the set of the first 10 natural numbers divisible by 4 can be represented in roster notation like: A = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40}.

What is Set Roster Notation in Sets?

Roster notation is one of the most simple techniques to represent the elements of a set. A comma-separated list of elements written within a pair of curly brackets is called the roster notation.

What are Roster Form and Set Builder Form?

In the roster form, the elements (or members) of a set are listed in a row inside the curly brackets separated by commas whereas in a set-builder form, all the elements of the set, must possess a single property to become a member of that set. For example, a set consisting of all even positive integers less than 11 is represented in roster form as {2, 4, 6, 8, 10} and in set-builder form, it is represented as {x | x ∈ N, x is even, x < 11}.

How to Express a Set in Roster Form?

In roster notation, the elements of a set are represented in a row surrounded by curly brackets and if the set contains more than one element then every two elements are separated by commas.

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