 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says the figure shows the relationship between the sets B and Q. Write this relation first the set builder form and second in the roster form. Write its domain and range. So first let us learn what is the relation between two non-empty sets. Suppose we have any two sets A and B. In a relation the non-empty set A to the non-empty set B is a subset of A cross B. That is the Cartesian product of A and B. And A cross B have all the ordered pairs X and Y such that X belong to A, Y belong to B. And this subset is derived by describing a relationship between the first element and the second element of the ordered pair A cross B. And here we are given the visual representation and with the help of this we will describe the relationship between the first element and the second element of the ordered pair in R and then represent it algebraically in the set builder form. Here we will give a specific rule of the relationship and in the roster form we will list the ordered pairs satisfying the rule. Also we will make use of the concepts of domain and the range of R remembering that the set of all the first elements of this ordered pair is called the domain and the set of all the second element of this ordered pair is called the range. So using these ideas we will solve the above problem so this is the idea. Now let us start with the solution and we are given the set B having elements 5, 6 and 7 and the set Q having elements 3, 4 and 5. Now from the adjoining figure it is clear that the image of element 5 is 3, 6 is 4 and 7 is 5. The relationship between the first element and the second element of the ordered pair is given by y is equal to x minus 2 where x are elements of P. Therefore in set builder form is equal to the set having all the ordered pairs x and y such that y is equal to x minus 2 and x is equal to 5, 6 and 7 which are elements of set P and the roster form set having elements all the ordered pairs 5, 3, 6, 4, 7, 5. So thus our answers are these two and also we are required to find the domain and range of R. The domain of R is the set of all the elements set of all the first element of these ordered pairs. So the first elements are 5, 6 and 7 and range of R is the set having all the second elements of these ordered pairs. And they are 3, 4 and 5. So let us write the required answers. First we are required to write in set builder form the relation R which is from P to Q and that is all the ordered pair x and y such that y is equal to x minus 2 for x belonging to P or x is equal to 5, 6 or 7. Also we have to write in the roster form and the other the pairs 5, 3, 6, 4 and 7, 5. This is the domain of R and this one is the range of R. So this completes the solution. Hope you enjoyed it. Take care and have a good day.