Relation OP Malhotra S.Chand ISC Class-12 Maths Solutions Ch-1

Relation OP Malhotra S.Chand ISC Class-12 Maths Solutions Chapter-1. Step by step Solutions of OP Malhotra SK Gupta Anubhuti Gangal S.Chand ISC Class-12 Mathematics with Exe-1  and Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

Relation OP Malhotra S.Chand ISC Class-12 Maths Solutions

Class:	12th
Subject:	Mathematics
Chapter  :	Ch-1 Relation  of Section -A

Board	ISC
Writer	OP Malhotra, SK Gupta, Anubhuti Gangal
Publications	S.Chand Publications 2020-21

---

-: Included Topics :- 

Exe-1 

Chapter Test

---

Relation OP Malhotra S.Chand ISC Class-12 Maths Solutions

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.

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.

---

Exe-1 

Relations OP Malhotra S.Chand ISC Class-12 Maths Solutions Chapter-1.

Question 1:

Consider the following properties of relations :

……………….

………………….

Question 2:

Write down relation which is

(i) Only transitive

(ii) Only symmetric

(iii) Only reflexive and transitive

(iv) Only symmetric and reflexive

Question 3:

…………………

………………….

………………..

Question 14:

Let f be the set of all integer ……………………………. is an equivalence relation.

Question 15:

Let f be the set of all integer and R be ………………………………… is an equivalence relation.

---

Types of Relation :

(i) Empty Relation:

A relation R in a set X, is called an empty relation, if no element of X is related to any element of X,
i.e. R = Φ ⊂ X × X

(ii) Universal Relation:

A relation R in a set X, is called universal relation, if each element of X is related to every element of X,
i.e. R = X × X

(iii) Reflexive Relation:

A relation R defined on a set A is said to be reflexive, if
(x, x) ∈ R, ∀ x ∈ A or
xRx, ∀ x ∈ R

(iv) Symmetric Relation:

A relation R defined on a set A is said to be symmetric, if
(x, y) ∈ R ⇒ (y, x) ∈ R, ∀ x, y ∈ A or
xRy ⇒ yRx, ∀ x, y ∈ R.

(v) Transitive Relation:

A relation R defined on a set A is said to be transitive, if
(x, y) ∈ R and (y, z) ∈ R ⇒ (x, z) ∈ R, ∀ x, y, z ∈ A
or xRy, yRz ⇒ xRz, ∀ x, y,z ∈ R.

(vi) Equivalence Relation:

A relation R defined on a set A is said to be an equivalence relation if R is reflexive, symmetric and transitive.

---

Chapter Test

Relations OP Malhotra S.Chand ISC Class-12 Maths Solutions Chapter-1.

Question 1:

(i) State the reason for the relation in the set …………….

(ii) Shoe that the relation  …………………

(iii)………………

(iv)………………

(v)………………

(vi)………………

Question 2:

Let R be a relation defined on the set of natural ………………………….. range of the relation R.

Question 3:

…………………

…………………

……………….

Question 9:

Let S be the set of all real numbers. then the relation

…………………….

……………………

Question 10:

Let the relation R on the set N of ……………………

………………….

………………….

-: End of Relations OP Malhotra S. Chand ISC Class-12 Maths Chapter-1 Solution :-

 

Return to :-  OP Malhotra S. Chand ISC Class-12 Maths Solutions

---

Thanks

Please share with your friends