 Hello and welcome to the session. In this session we discuss the following question which says, let a be equal to the set containing elements 369, b be equal to the set containing elements 61218 and r be the relation is half of from a to b, right r in roaster form represent r by an arrow diagram. Let's move on to the solution now. We have a set a with elements 369 and a set b with elements 61218 and we have r is the relation is half of from a to b. First of all we would write r in the roaster form to write r in the roaster form we form a set of ordered pairs in which the first component of the ordered pair would belong to the set a and the second component of the ordered pair would belong to the set b. And also the first component of the ordered pair is half of the second component of the ordered pair. Thus we can write r in the roaster form as a set of ordered pairs. Let's consider the first ordered pair in which the first component would be from set a. Let's take it as 3 and the second component would be from set b such that it would be 2 times of 3 or you can say 3 is half of the second component. Now 2 times of 3 would be 6 or you can say that 3 is half of 6. So in this way the first component and the second component are related to each other by the relation r that is is half of. Thus we get the second component of this ordered pair as 6. Now let's consider the next ordered pair in which we take the first component to be an element of set a. Let's take it as 6. Now 2 times of 6 would be 12. So 12 would be the second component which belongs to the set b or you can say that 6 is half of 12. So 612 is another ordered pair. Now consider the next ordered pair in which we take the first component as the element of set a which is 9 and 2 times of 9 is 18 which belongs to the set b or we can say 9 is half of 18. So thus we get this set of ordered pairs which is the relation r. So we have written the relation r in the roaster form in this way. Now next we are supposed to represent the relation r with arrow diagram. For this we would write the elements of the sets a and b in column form and we draw the arrows from elements of set a to the elements of set b satisfying the relation is half of. So we write the elements of set a in this column that is 3, 6 and 9 and the elements of set b in this column that is 6, 12, 18. Next we are supposed to draw arrows from elements of set a to the elements of set b such that the element of set a is half of the element of set b. Now as you can see that 3 is half of 6 so we would draw an arrow from 3 to 6. So we have drawn this arrow which indicates the direction from a to b. In the same way we have that 6 is half of 12 so we would draw an arrow from 6 to 12. This is the arrow from 6 to 12 then 9 is half of 18 so we would draw an arrow from 9 to 18. So this shows that 9 is half of 18 so this is the arrow diagram representing the relation r. So with this we complete the session hope you have understood the solution of this question.