 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says define a relation r on the set n of natural numbers by r is equal to the set of all ordered pairs x and y such that y is equal to x plus 5 and x is a natural number less than 4 where x and y belong to the set of natural numbers define this relation using roaster form, write the domain and the range. So first let us learn some simple definitions starting with the term relation. Suppose we have any two non-empty sets A and B then a relation r from the two non-empty sets A to B is a subset of the Cartesian product A cross B is a subset having ordered pair x and y such that x belong to A and y belong to B. Now the set of all the first elements of the ordered pair x and y is called the domain and set of all the second element of the ordered pair is called the range. So with the help of these definitions it will solve the above problem so there are key ideas. So let us now begin with the solution. Here we have to define the relation r on the set n of natural numbers where r is defined by the set of all the ordered pair x, y such that y is equal to x plus 5, x is a natural number less than 4 so x will take the values 1, 2 and 3 and x and y belongs to n so this is the relation we have to define. When x is equal to 1 y will be 1 plus 5 that is 6 and when x is equal to 2 y will take the value 2 plus 5 which is equal to 7 and when x is equal to 3 y will be equal to 3 plus 5 that is 8. So the relation r which is the subset of the Cartesian product of n cross n will have elements 1, 6, 2, 7 and 3, 8 and the domain of r will be the set of first element of these ordered pairs which are 1, 2 and 3 and range will have all those elements which are second in these ordered pairs that elements are 6, 7 and 8. So this relation is in the lost of form. That answers. I hope you enjoyed this session. Take care and bye for now.