Relations and Functions

2. Given, n (A) = 3

n (B) = 3 or B = {3,4,5}

So, number of elements in A* B = n (A* B) = n (A)* n (B) = 3 *3 = 9.

We have,

R= $\{\left(a,b\right):a\le b^2\}$ is a relation in R.

For $a\in R$ then is $b=a,a\le a^2$ is not true for all real number less than 1.

Hence, R is not reflexive.

Let $\left(a,b\right)\in R$ and a=1 and b=2

Then, $a\le b^2$ = $1\le 2^2$ = $1\le 4$ so, $\left(1,2\right)\in R$

But $\left(b,a\right)=\left(2,1\right)$

i.e., $2\le 1^2$ = $2\le 1$ is not true

so, $\left(2,1\right)\notin R$

hence, R is no

(i) We have, $R=\{\left(x,y\right):3x-y=0\}$ a relation in set A= $\{1,2,3..........14\}$

For $x\in A,y=3x$ or $y\ne x$ i.e.,

$\left(x,x\right)$ does not exist in R

$\therefore$ R is not reflexive.

For $\left(x,y\right)\in R,y=3x$

Then $\left(y,x\right)x\ne 3y$

So $\left(y,x\right)\notin R$

$\therefore$ R is not symmetric

For $\left(x,y\right)\in R$ and $\left(y,z\right)\in R$ . We have

$y=3x$ and $z=3y$

Then $z=3\left(3x\right)=9x$

i.e., $\left(x,z\right)\notin R$

$\therefore$ R is not Transitive

(ii) We have,

R=

The Class 12 Relations and Functions explores various types of Functions, Students can check main types dicussed in this chapter below;

• One-One Function (Injective)

• Onto Function (Surjective)

• One-One and Onto Function (Bijective)

• Identity Function

• Constant Function

• Inverse of a Function

• Composite Functions

Yes, We have updated our NCERT Class 12 Maths Relations and Functions solutions updated as per the latest CBSE 2025 syllabus.We have designed to provide best method of problem-solving which ensures better scoring capabilty of students.These updated solutions help students to do self-preparation, and

Students can find accurate NCERT Solutions for Class 12 Maths Relations and Functions on our website Shiksha.com. We provide step-by-step explanations that are easy to understand and follow the latest CBSE 2025 syllabus and exam pattern. Whether Students are preparing for board exams orfor Compeptiv

An inverse of a function does just opposite work as the original function does in other words it essentially "undoes" what the original function does. If a function f maps an input x to an output y (written as f (x) = y),

 then its inverse function is denoted as  f? ¹ (y) and&nbs

There are several methods to represent the relations and functions, Students can check few of them below;

• Arrow diagrams: This methods useage mapping from one set to another with arrows.

• Ordered pairs: This method represents relations and functions in bracket form like (x, y).

• Graphical representation:

A relation deals with, how elements from any set  (A) are related to elements of another set (B). there are various form of relations, such as Reflexive, Symatric, Transitive and Equivalance. On the other hand, Functions are special case of Relations where every element in Set A is related to e

Relations and functions  of class 11 Maths acts as the backbone of higher-level math topics like calculus, set theory, and advanced algebra. Relations deals with how elements are connected through any particular law or rule from set A to set B. Functions deals with specific relations that produ