# RS Aggarwal Class 12 Chapter 1 Solutions (Relations)

RS Aggarwal Solutions for Class 12 Chapter 1 Relations** **consist of exercise-wise solutions to all the questions available in total 2 exercises. The topics covered in these set of solutions are – types of relations, equivalence relations, and equivalence class. You will find a variety of questions based on these topics along with detailed answers. The questions range from very short answer type questions to identification exercises for better understanding of the types of relations.

There are 2 exercises consisting of 12 and 13 questions respectively in 1A and 1B. These exercise solutions are prepared to assist you in extensive practice for your board exams. RS Aggarwal Solutions for Class 12 Chapter 1** **have been developed to provide you with a diverse set of problems to build your understanding. The symbols used to denote different sets are as per the notified standards and therefore very reliable.

The experts at Instasolv make sure that they use simple language and stick strictly to the guidelines of the Board. Solving these questions will help you respond quickly to the objective type questions in the competitive exams. You will also get an idea of the difficulty level of the questions asked, and thus you will have an opportunity to ace the competitive exams as well. By practising these RS Aggarwal Solutions for Class 12 Maths Chapter 1, you will be prepared to answer tough questions while progressing ahead.

## Topics Covered in RS Aggarwal Solutions for Class 12 Chapter 1 Relations

**Introduction to Relations:**

The concept of Relations in maths has a literal meaning i.e. two quantities *a* and *b *are related if they have an identifiable link or connection between them.

A relation R between *a* and *b* can be denoted as (a, b) ∈ R or *a *R *b.*

**Empty Relation:**

A relation in a set A with the elements of the same set A will be a subset of A x A. An empty relation would be one when the elements are not related to one another by a given relation R. It is denoted as ዋ. Therefore, R = ዋ ⊂ A x A.

**Universal Relation:**

A universal relation is when all the elements of the given set A are related to all the elements of A by a relation R. Hence, R = A x A.

The Empty Relation and the Universal Relation are oftentimes termed as trivial relations.

**Reflexive Relation:**

A reflexive relation is when each element *a* of the set A is related to all the elements by the relation R such that (a, a) ∈R, for every a ∈ A.

**Symmetric Relation:**

Asymmetric relation is when the elements a_{1 }and a_{2 }are related by R while a_{2 }and

a_{1}belonging to the relation R also hold true.

Therefore, for all a_{1}, a_{2 }∈ A, if (a_{1}, a_{2}) ∈ R;

It will imply that (a_{2}, a_{1}) R in asymmetric relation.

**Transitive Relation:**

If the elements of a set A, a_{1}and a_{2}belong to the relation R and a_{2}, a_{3}also belong

to R; then a_{1 }and a_{3 }belonging to R will also hold true.

Hence, for all a_{1}, a_{2}, a_{3 }∈ A, if (a_{1},a_{2}) ∈ R and (a_{2}, a_{3})∈ R;

It will imply that (a_{1},a_{3})∈ R, in a transitive relation.

**Equivalence Relation:**

If a relation R is all at once, that is, symmetric, reflexive as well as transitive, it is termed as an Equivalence relation.

**Equivalence Class:**

If R is an equivalence relation in a given set X, then the Equivalence class is given as [a] that comprises of a ∈ X such that X contains all elements b related to a.

While solving the exercise questions, to prove that a relation R is an equivalence relation, we will have to first establish that R is a reflexive, symmetric as well as a transitive relation.

**Highlights of Chapter 1 Relations**

- A relation R defines the identifiable link between the elements of the set X.
- The empty relation and universal relation are the two extreme variants of relations and are also known as trivial relations.
- When (a, a) ∈ R, for every a ∈ A, it is known as a reflexive relation.
- When for all a
_{1}, a_{2 }∈ A, if (a_{1}, a_{2}) R leads to a result such that (a_{2}, a_{1}) ∈ R; then R is a symmetric relation.

When for all a_{1}, a_{2}, a_{3} ∈ A, if (a_{1}, a_{2}) ∈ R and (a_{2}, a_{3}) ∈ R leads to a result such that (a_{1},a_{3}) ∈R then R is a transitive relation.

### Exercise Wise Discussion of RS Aggarwal Solutions for Class 12 Chapter 1 Relations

- The exercise solutions 1A will require you to find the range and domain of the set of the relation R.
- You will also have to define your understanding of the range and domain of R as you will proceed further.
- In the later part of 1A and 1B, you will have to prove the equivalence of a relation and the reflexivity, symmetry and transitivity of the relations respectively.
- You can solve all the important questions for your school and board exam, taking assistance from the solutions curated by the masters as Instasolv.
- The solutions in RS Aggarwal Class 12 Maths Solutions by Instasolv are apt for subjective exams and will also help you to arrive at the answers easily for the objective type question paper.
- Practising these exercise solutions will help you amplify your marks exponentially, therefore it is highly recommended that you go through them thoroughly before your exams.

## Benefits of RS Aggarwal Solutions for Class 12 Maths Chapter 1 by Instasolv

- The proficient team of Instasolv has prepared the solutions employing the simplest language possible with an objective to help you build strong fundamentals for your higher studies.
- You will find absolutely no issues regarding the compatibility of solutions according to your level of understanding at Instasolv.