 Hi and welcome to the session. I am Asha and I am going to help you with the following question with C's. Let A be a set having elements 1, 2, 3, 4 and 6. Let R be a relation on A defined by the set of all ordered A, B such that A and B are elements of A and B is exactly divisible by A. First is write R in Roaster form. Second is find the domain of R and the third one is find the range of R. So first let us learn what is a relation. Suppose we have any two non-empty sets A and B, then a relation from A to B is a subset of the Cartesian product A cross B where A cross B is the set of all ordered A x, y such that x is the element of A and y is the element of B. The subset is derived by describing the relationship between the first element and the second element of the ordered A cross B. And the second element is called the image of the first element and the set of all of the ordered A is called the domain and the set of all second element of the ordered A is called the range. So these definitions have a key idea that we are going to use in this problem to solve it. Let us now start with the solution and here we are given a set A having elements 1, 2, 3, 4 and 6. We have to define R in a Roaster form where R is a relation defined on A and the relation R is from set A into itself. R is set of all ordered A and B such that A and B belong to set A and B is exactly divisible by A. So we have to define all the ordered pairs such that the second element of the ordered pairs exactly divisible by the first element. These are divisible by 1. So first we have to order pairs 1, 1, 1, 2, 1, 3, 1, 4, 1, 6, divisible by 2, also 4 is divisible by 2, 6 is divisible by 2. Now let us proceed on to the third element. Now 3 is divisible by 3, 4 is not divisible by 3 and then we have 6 is divisible by 3. And lastly 4 is divisible by 4 and 6 is divisible by 6. So hence the Roaster form of the relation R is 1, 1, 1, 2, 1, 3, 1, 4, 1, 6, 2, 2, 2, 4, 2, 6, 3, 3, 3, 6, 4, 4 and 6, 6. So this is the solution of the first part and now proceeding on to the second part where we have to find the domain of R. Now with a set of all first elements of these ordered pairs is the domain of R. So domain of R will be a set having elements 1. Now the first element of this ordered pair is 2 and the first element is 3 and the first element is 4 and 6. So this is the domain of R and the third is to find the range of R. This is the set of all the second element of these ordered pairs which are 1, 2, 3, 4 and 6. So this completes the solution. Hope you enjoyed it. Take care and have a good day.