# Relations and functions

# NCERT Solutions for Maths - Relations and Functions by Sonika Anand Academy

**Video Lectures**

Domain and Range of a function

How to find cartesian product of two sets A×B

Representation of two sets using arrow diagram

Find a relation between two sets where one set is cube root of other

How to find number of relations from one site to another

How to find number of elements in relation from a to b

Content of Lecture

How to find domain and range and codomain of any function

How we will distinguish between one one and many one function

It is also explained as what is the other name of one one function that is one one function is also named as injective function whereas many one function is also known as surjective function

A function as both one one and onto then it is also known as bijective function

what are the different conditions which are satisfied when any function is one one function and when it is many one function

How meni define whether a function is strictly increasing or decreasing using graph method

How to find the number of relations in between two given sets that is what is the formula to find the number of relations between two sets

What is the formula to find the number of mappings from one set to another

Types of Functions

Inverse of a function

What is an invertible function and how to find inverse of any function os explained in given lecture

Questions discussed in next lecture --

How to find

subset ,proper subset

cardinal number of a set

Subset =2^n

Proper subset = 2^n-1

Find number of subset

If A={x:x = 3x+1,2<=x<=5}

Set is x= {2,3,4,5}

A={7,10,13,16}

So subset =2^n = 2⁴= 2×2×2×2= 16

How to find number of Relations from A to B containing m and n elements

(2)^m×n

If two finite sets A and B have m and n elements total number of relations is 64 find the value of m and n

If two sets have m and n elements and total number of subsets of first set is 56 more than subset of B find the value of m and n

## Set Theory

**Multiple choice questions**

1) The relation is defined on the set

A= {1,2,3,4,5} by R={(a,b):|a^2-b^2|<16} is given by

a) {(1,1),(2,1),(3,1),(4,1),(2,3)}

b) {(2,2),(3,2),(4,2),(2,4)}

c){(3,3),(4,3),(5,4),(3,4)}

d) none of these

Ans

d )none of these

2) The smallest equivalence relation on the set A= {1,2,3}is

a) {(1,1),(2,2),(3,3)}

b){(1,1)}

c){(1,1),(2,1),(3,1),(2,2),(2,3),(3,2)}

d) none of these

Ans

a) {(1,1),(2,2),(3,3)}

3) If A = {1,2,3}and B ={1,4,6,9} and R is a relation from Ato B defined X is greater than y the range of R is

a) {1,4,6,9}

b){4,6,9}

c) {1}

d) none of these

Ans

c) {1}

4) A relation R is define from { 2,3,4,5 } {3,6,7 ,10} by x R y = x is relatively prime to y then domain of R is

a) {2,3,5}

b.){3,5}

c ) {2,3,4}

d) {2,3,4,5}

Ans

a) {2,3,5}

5) R is a realation from {11,12,13} to {8,10,12} defined by y=x-3 Then inverse of R is

a) {(8,11),(10,13)}

b.) {(11,8),(13,10)}

c) {(10,13),(8,11),(8,10)}

d) none of these

Ans

a) {(8,11),(10,13)}

6) Let R be a relation on the set N of natural numbers defined by n R m iff n divides m Then R is

a) Reflexive and symmetric

b) Transitive and symmetric

c) Equivalence

d) Reflexive,transitive,but not symmetric

Ans

d)

7) Maximum number of equivalence relations on the set A={1,2,3} is

a) 1

b). 2

c) 3

d) 5

Ans

d ) 5

8) If the set A contains 7 elements and set B contains 10 elements then number of one one functions from A to B is

Ans b)

9) If A = {1,2,3,.....n} and B = {a,b}.Then number of subjections from A to B is

Ans (b)

10) If f(x)= px/x+1,xis not equal to -1 then for what values of p f(f(x))= x

a) √2

b) -√2

c) 1

d) -1

Ans

d ) -1