# Representation of Sets in Mathematics

Topic discussed in this video:

• Representation of sets in math
• Roster form / Listing Method
• Set-builder form / Property Method

To understand the representation of sets, let’s get back to its definition.

A set is a well-defined collection of objects of the same kind.

Here, the phrase collection of objects gives us the idea that we can make a list of all the objects. That’s why the first method is known as the listing method. The other name for the listing method is the roster form of the set.

Secondly, the phrase objects of the same kind give us the idea that all the objects in that collection possess a common property and we can represent the set by that common property. That’s why the second method is known as the property method. The other name for the property method is the set-builder form of the set.

Let’s take an example “a collection of the first five natural numbers” to understand the two forms in detail.

As we know, a collection of the first five natural numbers will always have 1, 2, 3, 4, and 5. In roster form, we make a list of these objects like this:
Objects are also known as elements of sets. In roster form, elements are always separated by commas and always enclosed within curly braces {}.
Generally, we usually denote sets by capital letters and elements by small letters. So, if I denote the set by A, then the roster form will look like this:

Before we discuss the set-builder form, there are two important points regarding the roster form that you should remember……

# Practice Questions related to Sets

Topic discussed in this video:

• Questions related to sets in Math for better understanding of its definition

Question 1. Which of the following are sets? Justify your answer.
(i) The collection of all the months of a year beginning with the letter J.
(ii) The collection of ten most talented writers of the world.
(iii) The collection of all the English alphabet.
(iv) The collection of good students in a class.
(v) The collection of beautiful flowers in a garden.
(vi) A team of eleven best-cricket batsmen of the world.
(vii) The collection of all the natural numbers less than 100.
(viii) A collection of books written by J. K. Rowling.
(ix) The collection of all even integers.
(x) A collection of most dangerous animals of the world.

# Meaning of Set in Mathematics

Questions discussed in this video:

• What is Set?
• Use of Set in Practical Life?
• Types of Sets in practical life?
• What is set in Mathematics?

We often use the word set in our day to day life. For example, we usually have dinner sets in our homes and as the name suggests, a dinner set is a collection of cups, plates, dishes, saucers etc., used for serving food and dinning. So, as with a dinner set, a set is a collection of objects of same kind. And this set can be of two types in our practical lives.

For instance, if I asked you to create a collection of all the songs recorded by Lady Gaga, you can easily do that with the help of some research and the internet. But, instead of a collection of all songs, I asked you to create a collection of top five songs recorded by Lady Gaga. Now, collection of all songs and collection of top five songs they both are collections, they both are sets but there’s a big difference between both.
A collection of all songs will always be the same, whether you will create that collection or I will create that collection, that collection will always have same songs. Yeah, the order in which we collect these songs can be different but the overall collection will always be the same…..