** Relation and Mapping** OP Malhotra S.Chand ISC Class-11 Maths Chapter-2. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-2 (a), Exe-2 (b), Exe-2 (c), Exe-2 (e), Exe-2 (f) and Exe-2 (g) Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

## Relation and Mapping OP Malhotra S.Chand ISC Class-11 Maths Solutions

Class: | 11th |

Subject: | Mathematics |

Chapter : | Ch-2 Relation and Mapping of Section -A |

Board | ISC |

Writer | OP Malhotra |

Publications | S.Chand Publications 2020-21 |

-: Select Topics :-

### Relations and Functions Class 11 Chapter 2

Before we start learning about relations and functions class 11, let us go through some basics of sets. As we learned, a set is a collection of objects or elements. You have also learned about the empty set, universal set and all the other types in sets for class 11

#### Cartesian Product of Sets

Suppose there are two non-empty sets A and B. So, the cartesian product of A and B is the set of all ordered pairs of elements from A and B.

A × B = {(a,b) : a ∊ A, b ∊ B}

Let A = {a_{1}, a_{2}, a_{3}, a_{4}} and B = {b_{1}, b_{2}}

Then, The cartesian product of A and B will be;

A × B = {(a_{1}, b_{1}), (a_{2}, b_{1}), (a_{3}, b_{1}), (a_{4}, b_{1}), (a_{1}, b_{2}), (a_{2}, b_{2}), (a_{3}, b_{2}), (a_{4}, b_{2})}

Example: Let us say, X = {a,b,c} and Y = { 1,2,3}

**Definition of Relations:**

A relation R is the subset of the cartesian product of X x Y, where X and Y are two non-empty elements. It is derived by stating the relationship between the first element and second element of the ordered pair of X × Y. The set of all primary elements of the ordered pairs is called a domain of R and the set of all second elements of the ordered pairs is called a range of R.

#### Functions

A relation ‘f’ is said to be a function, if every element of a non-empty set X, has only one image or range to a non-empty set Y.

Or

If ‘f’ is the function from X to Y and (x,y) ∊ f, then f(x) = y, where y is the image of x, under function f and x is the preimage of y, under ‘f’. It is denoted as;

f: X → Y.

### Functions

A relation ‘f’ is said to be a function, if every element of a non-empty set X, has only one image or range to a non-empty set Y.

Or

If ‘f’ is the function from X to Y and (x,y) ∊ f, then f(x) = y, where y is the image of x, under function f and x is the preimage of y, under ‘f’. It is denoted as;

f: X → Y.

**Inverse of Relation**

For any two non-empty sets A and B. Let R be a relation from a set A to a set B. Then, the inverse of relation R, denoted by R^{-1} is a relation from B to A and it is defined by

R^{-1} ={(b, a) : (a, b) ∈ R}

Domain of R = Range of R^{-1} and

Range of R = Domain of R^{-1}.

**Functions**

A relation f from a set A to set B is said to be function, if every element of set A has one and only image in set B.

In other words, a function f is a relation such that no two pairs in the relation have the first element.

**Real-Valued Function**

A function f : A → B is called a real-valued function if B is a subset of R (set of all real numbers). If A and B both are subsets of R, then f is called a real function.

**Some Specific Types of Functions**

Identity function: The function f : R → R defined by f(x) = x for each x ∈ R is called identity function.

Domain of f = R; Range of f = R

**Constant function:** The function f : R → R defined by f(x) = C, x ∈ R, where C is a constant ∈ R, is called a constant function.

Domain of f = R; Range of f = C

**Polynomial function:** A real valued function f : R → R defined by f(x) = a_{0} + a_{1}x + a_{2}x^{2}+…+ a_{n}x^{n}, where n ∈ N and a_{0}, a_{1}, a_{2},…….. a_{n} ∈ R for each x ∈ R, is called polynomial function.

**Rational function:** These are the real function of type 𝑓(𝑥)𝑔(𝑥), where f(x)and g(x)are polynomial functions of x defined in a domain, where g(x) ≠ 0.

**The modulus function:** The real function f : R → R defined by f(x) = |x|

or

for all values of x ∈ R is called the modulus function.

Domaim of f = R

Range of f = R^{+} U {0} i.e. [0, ∞)

**Signum function:** The real function f : R → R defined

by f(x) = |𝑥|𝑥, x ≠ 0 and 0, if x = 0

or

**Exe-2(a),**

### Relation and Mapping OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page No-(2-6)

** Exe-2 (b),**

Relation and Mapping OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page No-(2-11)

** Exe-2 (c),**

Relation and Mapping OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page No-(2-19)

** Exe-2 (d),**

### Relation and Mapping OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page No-(2-28)

**Exe-2 (e),**

Relation and Mapping OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page No-(2-36)

**Exe-2 (f)**

### Relation and Mapping OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page No-(2-43)

** Exe-2 (g)**

#### Relation and Mapping OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page No-(2-57)

-: End of **Relation and Mapping** Solution :-

Return to :- OP Malhotra S. Chand ISC Class-11 Maths Solutions

Thanks

Please share with your friends

yes this is very helpfull pls read it

thanks for your positive response to encourage us

team

icsehelp

why is none of the images loading

dear student / well wisher / Teacher

the previous version of 2020-21 has been removed because council has decided to start new session from 1st April Therefore we are upgrading the solutions of 2021-22 editions

Sorry for inconvenience

thanks

team icsehelp

can you please reupload these images for now?

now full chapter PDF showing/ working

please visit again for analysis

Could you kindly share the earlier solutions as they are really helpful for our upcoming final exams.

new solutions uploaded soon

when will it be uploaded by?

start from Monday

Why …our exams are not yet over

Dear student / well wisher / Teacher

Sorry for inconvenience but all chapter solutions will be uploading soon

Thanks

team icsehelp

uploaded again very soon

uploaded soon

Dear icse help, please upload the solutions as it is very helpful , and exams are going to begin very soon

Thank you

yes very soon

I am to see the solutions

the all chapter solutions will be available in April

april ?2020 or 2021 or 2022

sorry for mis typing

pls upload the solutiond I HAVE MY EXAM TOMMORROW

now full chapter showing now please visit again

Sir solution are not able to open only exercise name is there no solution

uploaded again soon

live very soon

Sir, u have not uploaded the solutions. U said that u will uploaded till April…

All chapter PDF solutions showing / working completely

please visit again for analysis

Where are the solutions?

sure will be upload it before sem-1 start if in syllabus

sir its been 5 months when will it be uploaded?

All chapter PDF solutions showing / working completely

please visit again for analysis

Why pages are not available??? Plzz make it available as soon as possible

now full chapter PDF showing/ working

please visit again for analysis