Roster Form

The roster Form of a set, also known as tabular form, is a way of representing a set by listing all its elements in a row and surrounded by curly brackets {}. If the set has more than one element, they are separated by commas and enclosed in curly brackets. For example, the set K of the first six even numbers is written in roster form as K = {2, 4, 6, 8, 10, 12}. 
 

In addition to the roster form, sets can also be represented using a set-builder form notation, which describes the properties of the elements. The set builder form is used to conditionally express the set. For example, a set of the English alphabet that can be written in set-builder form as {x: x is a letter of the English alphabet}. Here are some differences between the roster and set builder forms:
 

The roster form lists the elements of a set within curly brackets, presenting them in a simple and easy-to-read format. The Venn diagram is a visual tool used to show the relationships between two or more sets by using overlapping circles to represent shared and distinct elements. The overlapping region shows what elements are common and unique. Roster form is used in Venn diagrams to list the elements of each set within curly brackets, separated by commas, {}.  Let’s see how the roster form is used in the Venn diagram.

Example:

Consider two overlapping circles representing sets A and B.

 A =  {2, 4, 6, 8}
 B =  {4, 8, 12, 16}
 

The intersection of A and B contains  {4, 8}
The union of A and B {2, 4, 6, 8, 12, 16}. The roster form is used to list the elements of sets A and B, as well as their intersection and union, which can then be represented in a Venn diagram.
 

 Roster form is simple and easy to understand, but it has several limitations, especially when working with large or infinite sets. For large sets, such as one containing hundreds of elements, listing every item becomes impractical, time-consuming, and difficult to read. The format takes up too much space and becomes inefficient. For infinite sets, such as the set of natural numbers, roster notation cannot list all elements. Instead, it shows only a few initial values followed by an ellipsis: {1, 2, 3, 4, 5, …}. This gives only a partial representation, not the full set. 

The roster form is not only used in mathematics, but it also has practical applications in everyday life. In many real-life situations, we use the roster form to organize or list items, often without even realizing it.

• Representing Game Score: The roster form can be used to list the scores of players in a basketball game. For example, if three players scored 5, 15, and 18 points, their scores can be written in roster form as G = {5, 15, 18}.

• Tracking Schedule: The roster form can also be used to schedule events or activities. For example, if a student has classes on Monday, Tuesday, Wednesday, this can be written in roster form as S = {Monday, Tuesday, Wednesday}.

• Data Management: In database management, the roster form can be used to represent a list of specific entries from a dataset, such as user IDs, product names, or registered email addresses.

• Organizing Team: The roster form can be used to represent the members of a team by listing their names in a set. This helps in organizing and identifying the team of participants.

• Managing the Contacts: The Roster form can be used to represent a small group of contacts by listing their names (or phone numbers, email addresses, etc.) in a set. This is useful for organizing and viewing specific contact lists easily.