Roster Form
Roster notation of a set is a simple mathematical 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, 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.  FAQs on Roster Form 
What is Roster Notation?
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. For example, if A is the set of the first 10 natural numbers so it can be represented by: A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Roster Form Set Notation
A method of listing the elements of a set in a row with comma separation within curly brackets is called the roster notation. An example of the roster form in set notation is given below:
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 stepwise.
 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 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 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.
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 the null set is represented by ∅.
 The roster notation is not used for too much data.
Related Topics on Roster Form
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 = 2n^{2}  1, where n ∈ N and n < 5} in roster form.
Solution: The elements of set A are:
 For n = 1, 2n^{2 }− 1 = 2 × 1^{2} −1 = 1
 For n = 2, 2n^{2 }− 1 = 2 × 2^{2 }− 1 = 7
 For n = 3, 2n^{2 }− 1 = 2 × 3^{2 }− 1 = 17
 For n = 4, 2n^{2 }− 1 = 2 × 4^{2 }− 1 = 31
 For n = 5, 2n^{2 }− 1 = 2 × 5^{2 }− 1 = 49
Answer: A = {1, 7, 17, 31, 49}
FAQs on Roster Form
What is Roster Form in Set Theory?
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 are represented like: A = {2, 4, 6, 8, 10}.
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 setbuilder form, all the elements of the set, must possess a single property to become the 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 setbuilder 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.
What is Roster Notation in Sets?
Roster notation is one of the most simple techniques to represent the elements of a set. A method of listing the elements of a set in a row with comma separation within curly brackets is called the roster notation.
What is Roster Form Example?
An example of roster form: 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}.
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