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

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 or 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 :-

Exe-2(a),

Exe-2 (b),

Exe-2 (c),

Exe-2 (d),

Exe-2 (e),

Exe-2 (f)

Exe-2 (g)

### 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 = {a1, a2, a3, a4} and B = {b1, b2}

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

A × B = {(a1, b1), (a2, b1), (a3, b1), (a4, b1), (a1, b2), (a2, b2), (a3, b2), (a4, b2)}

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) = a0 + a1x + a2x2+…+ anxn, where n ∈ N and a0, a1, a2,…….. an ∈ 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),

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),

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 :-

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### 33 thoughts on “Relation and Mapping OP Malhotra S.Chand ISC Class-11 Maths”

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• 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
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• now full chapter PDF showing/ working

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

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• Why …our exams are not yet over

• Dear student / well wisher / Teacher
Thanks
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3. Dear icse help, please upload the solutions as it is very helpful , and exams are going to begin very soon
Thank you

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4. 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

5. pls upload the solutiond I HAVE MY EXAM TOMMORROW

• now full chapter showing now please visit again

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

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

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8. Where are the solutions?

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

9. sir its been 5 months when will it be uploaded?