The roster or tabular method is a way to represent a set by explicitly listing all of its elements within curly braces { }. This method is most commonly used when the set has a finite number of elements and is relatively small. Here's how you can present a set using the roster or tabular method:

Roster Method Example:-

Suppose you want to represent a set called "A" that contains the days of the week. You can list all the days within curly braces like this:

A = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

In this example, "A" is the name of the set, and all the days of the week are explicitly listed as its elements.

Tabular Method Example:-

The tabular method is a variation of the roster method that can be particularly useful when you need to represent sets with additional information or properties. It involves creating a table or matrix where each row represents an element of the set, and columns can be used to provide additional details about the elements.

For example, let's say you want to represent a set "B" that contains information about people's names and ages:

B = {
       | NameAge |
       | Alice  |  30  |
       |  Bob  |  25  |
       | Carol  |  35  |
       | David  |  28  |

In this tabular representation, "B" is the name of the set, and each row represents an element with two properties: Name and Age. You can include as many columns as needed to describe the elements of the set fully.

In a tabular format, you can represent sets with multiple properties or attributes for each element. Here's an example of a set represented in a tabular format:

Example 1:- Set of Colors

  {Red, Blue, Green, Yellow, Purple}

In this example, the set contains the colors Red, Blue, Green, Yellow, and Purple. These elements are listed explicitly within the curly braces.

Example 2:- Set of Even Numbers Less Than 10

  {2, 4, 6, 8}

This set includes the even numbers 2, 4, 6, and 8, all of which are listed directly in the set.

Example 3:- Set of Days in a Week

  {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

Here, the set contains the seven days of the week, each of which is listed as an element.

Example 4:- Set of Fruits

  {Apple, Banana, Orange, Mango, Grape}

This set represents a collection of fruits, with each fruit listed as an element of the set.

Example 5:- Set of Students with Their IDs

       | Student Name | Student ID |
       |      Alice      |    12345    |
       |      Bob       |    23456     |
       |      Carol      |    34567    |
       |      David      |   45678     |

In this example, the set consists of students, and for each student, both their name and student ID are listed in a table.

Example 6:- Set of Natural Numbers Less Than 10

  {1, 2, 3, 4, 5, 6, 7, 8, 9}

Example 7:- Set of U.S. States in the West Coast

  {California, Oregon, Washington}

This set includes the U.S. states located on the West Coast, and the names of these states are listed as elements.

Example 8:- Set of Primary Colors

  {Red, Blue, Yellow}

Here, the set consists of the primary colors: Red, Blue, and Yellow, which are listed as elements of the set.

Example 9:- Set of Planets in the Solar System

  {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}

This set contains the planets in our solar system, and each planet's name is explicitly listed within the set.

The roster or tabular method is a straightforward way to represent sets with a finite number of elements or elements that can be easily enumerated. It provides a clear and complete list of all the elements in the set.