 Hi and welcome to the session. I am Asha and I am going to help you with the following question that says if a is a set having elements 1, 2, 3 and 5 and b is a set having elements 4, 6 and 9 define a relation r from a to b by r is equal to the set of all the ordered pairs x and y such that the difference between x and y is odd and x and y are elements of a and b respectively write r and roster form. So first let us learn some simple definitions starting with the term relation if a and b are any two non-empty sets the relation from a to b is a subset of the Cartesian product a cross b where the elements of a cross b are the ordered pairs of the type x cross y where x belong to a and y belong to b so this is the roster representation of the relation r which is from a to b so this definition is 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 have set a having elements 1, 2, 3 and 5 and the set b have elements 4, 6 and 9 and the relation r is having all the ordered pairs x and y such that difference of x and y is odd x belong to the set a and y belong to the set b the difference between x and y is odd therefore if x is odd then y is even y is odd then x should be even so y is the versa therefore the roster representation of the relation r will be if x is 1 then y should be even since x is an odd number 1 being an odd number so we will find all the even numbers from this set therefore and if x is 2 if 2 being an even number we will have to find all the odd numbers from the set b to make the ordered pairs and that is 9 next number is 3 being an odd number so the 2 even numbers are 4 and 6 so the pairs are 3, 4 and 3, 6 and then we have 5 which is again an odd number the even numbers are 4 and 6 so this is the relation r which is the subset of the Cartesian product 8 plus p so this completes the solution hope you enjoyed it take care and bye for now