 Hello and welcome to the session. In this session, we will learn about relations and their representation. First of all, let us review what is order pair. Order pair is a pair of objects whose components occur in a specific order. It is denoted by, that is, the elements which are related are put inside the parenthesis and separated by a comma. For example, the order pairs are 1 1, 1 2, 2 1. Now, let us review what is a relation. A relation is a set comprising which satisfies a certain rule. Now, let us take some order pairs 1 1, 2 1, 4 2 and 3 1 and let the relation r is equal to the set containing order pair x y such that x is greater than y. Now, the order pairs which are satisfying this relation in order order pairs, the first component is greater than the second component. And here the relation is mentioned to us as the set containing the order pair x y in which the first component is greater than the second component. So, the order pairs satisfying this relation are 2 1, 3 1. So, we can write r is equal to containing the order pair 2 1, 4 2 and 3 1. Therefore, the relation is a set of order pairs which are satisfying a certain given rule. Now, the components of the order pairs is called equal to the set containing the first components of the ordered pairs. So, it is a set containing the elements 2, second components. So, it is equal to the set containing the elements 1, represented by Osterfaq error driver in the equation form. Now, let us take a relation which is equal to the set containing the order pair x y such that x is equal to 4 y are natural numbers less than 10. We have to find first of all the order pairs which are satisfying this relation by our natural numbers less than 10. So, first of all for y is equal to 1, we have x is equal to 4 into 1 which is equal to 4. So, for y is equal to 1, x is equal to 4. Now, for y is equal to 2, x is equal to 4 into 2 which is 8. So, we are getting for y is equal to 3 into 3 which is equal to 12. Now, in this case we do 12 but here it is mentioned that x and y are natural numbers less than 10. So, we will not take this case and we will take only this relation in the Roasterfaq relation r as the set of ordered pairs. So, here r is equal to the set containing the ordered pairs 4, 1, equation r which was given to us and this is the representation of this relation r in the Roasterfaq. Present this relation by an error diagram on one side. Now, domain is the set of the first components of the ordered pairs. So, it is 4 and 8. So, we are writing 4 and 8 here and the range is the set of the second components of the ordered pairs. So, we will write 1 and 2 here. Now, in the error diagram add and connect it by arrows. So, it is related with 1. So, we will connect 4 and 1 with arrow and 8 is related with 2. So, it will 2 by 2 4 times 2. Now, let us see how to represent this relation equation form. The second component that you can see here equation form, we can write this relation as the next is to represent the relation by a rule. Now, the relationship. Now, here the second component is this component is 4 times y. Therefore, we can write. So, this is the relation we have learned about. We have enjoyed the session.