 Hello and welcome to the session. In this session we discuss the following question which says, let set AB equal to the set containing the elements 2, 4, 6, 8, 10 and set B be equal to the set containing the elements 1, 2, 3, 4, 5 and R be the relation is 2 times of form the relation R from A to B find the domain and range of R. A relation is a set of ordered pairs. Now we define the domain and range of a relation so we have the set of first components of ordered pairs is called the domain and the set of second components of ordered pairs is called the range. We also have a relation R from a non-empty set A to a non-empty set B is a rule by which elements of set A can be associated with elements of set B. This is the key idea that we would use for this question. Let's proceed with the solution now. We have the set A as the set containing the elements 2, 4, 6, 8 and 10 and a set B with elements 1, 2, 3, 4, 5 and we have R is the relation is 2 times of and we are supposed to form a relation R from set A to set B. So according to this definition we have that a relation R from set A to set B is a rule by which elements of set A can be associated with elements of set B. So the relation R would be the set of ordered pairs since we know that a relation is a set of ordered pairs and these ordered pairs would be formed such that the two components of the ordered pair satisfy the given relation R. So the first ordered pair would be 2, 1. This 2 is from the element of the set A and we know that 2 is 2 times of 1 and so this 1 is from the element of set B. So in this way in this ordered pair element of set A is related to or is associated with the element of set B using the relation R which is 2 times of. So in the same way the next ordered pair formed would be 4, 2 since 4 is 2 times of 2 and this 4 is from the set A and 2 is from the set B. Next ordered pair would be 6, 3 since 6 is 2 times of 3, 6 is from the set A and 3 is from the set B. The next ordered pair would be 8, 4, 8 is from the set A and 4 is from the set B and 8 is 2 times of 4. The next would be 10, 5. 10 is from set A, 5 is from set B and 10 is 2 times of 5. So in this way we get this set of ordered pairs. So thus we have the relation R defined in this way. So we have formed the relation R from A to B. Next we are supposed to find the domain and range of R. From the key idea as you know we have that the set of first components of ordered pairs is called the domain and the set of second components of ordered pairs is called the range of the given relation. Now from this relation R let's make a set of the first components of the ordered pairs. So that would be 2, 4, 6, 8, 10. So this would be the domain. Now let's make a set of the second components of the ordered pairs which is 1, 2, 3, 4, 5. This would be the range. Thus we can say that domain of the relation R is the set with the elements 2, 4, 6, 8, 10 and the range of the relation R is the set containing the elements 1, 2, 3, 4, 5. Thus we have got the domain and range of the given relation R. So this completes the session. Hope you have understood the solution of this question.