**Kc Sinha Mathematics Class 12 Chapter 1 Relation Solutions** are prepared by the teacher of Class 12 Mathematics in brief. According to the **Class 12 Maths syllabus**, Some chapters of class 12th maths are very important for the board exam. According to the topper students of Bihar Board Exam, **Kc Sinha Maths Book** is very important for board students. If you want to learn the topics and subtopics of every chapter of **Class 12 Kc Sinha Mathematics Book** in brief. You can check our article “Kc Sinha Solution Class 12 Maths PDF Part 1”.

As you know, **Kc Sinha Maths Class 12 Chapter 1** is the Relations chapter. Let me say to you that the relations chapter is difficult to read without a set theory. So, I am telling to you that you should learn the set theory of **Kc Sinha Class 11 Maths** Book in brief. All the questions of **Kc Sinha Mathematics Class 12 Chapter 1 relation solutions** are not available in the free course.

## Kc Sinha Class 12 Chapter 1 Relation

Question No 1 (i) and (ii) Solution of Kc Sinha Class 12th Mathematics Chapter 1 are following

**(i) Let A = {1, 9}, B = {5, 13} and R = {(a, b) : a ∈ A, b ∈ B and a — b is divisible by 4. Show that R is an universal relation from A to B.**

As we know, in this question R is written in the set builder form. So, first of all, I write the possible form of set A to set B is in the roaster form. A × B = {(1, 5), (1, 13), (9, 5), (9, 13)}. In the roaster form of A × B, you can see that R is a universal relation. So, you can say R is a universal relation on A × B.

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**(ii) Let A = {1, 5}, B = {3, 7} and R = {(a, b) : a ∈ A, b ∈ B and a — b is divisible by 4. Show that R is an empty relation from A to B.**

As we know, in this question R is written in the set builder form. So, first of all, I write the possible form of set A to set B is in the roaster form. A × B = {(1, 3), (1, 7), (5, 3), (5, 7)}. In the roaster form of A × B, you can see that R is an empty relation. So, you can say R is an empty relation on A × B.

### Class 12 Maths Relation Chapter Solution

**Let A be the set of all students of a boys school. Show that the relation R in A given by**

(i) R = {(a, b) : a is sister of b} is empty relation in A.

(ii) R’ = {(a, b): the difference between heights of a and b is less than 3 metres} is the universal relation in A.

(i) The relation R is an empty relation because all elements of set A are boys. In that case, a is not the sister of b because a and b both are boys. So, you can say R is an empty relation on A.

(ii) The relation R is a universal relation because the difference between heights of a and b is less than 3 metres. It is possible. So, you can say R is a universal relation on A.