(D) The given relation is $S = \{(a, b) : a < b^2\}$.$1$. For reflexivity: Is $(a, a) \in S$? That is,is $a < a^2$? If we take $a = 0.5$,then $0.5 < (

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(D) The given relation is $S = \{(a, b) : a $1$. For reflexivity: Is $(a, a) \in S$? That is,is $a $2$. For symmetry: Does $(a, b) \in S \implies (b, a) \in S$? Let $(1, 2) \in S$ because $1 $3$. For transitivity: Does $(a, b) \in S$ and $(b, c) \in S \implies (a, c) \in S$? Let $(3, 2) \in S$ $(3 Since the relation is neither reflexive,nor symmetric,nor transitive,it is not an equivalence relation.

Class 12 Mathematics Relation and Function Types of Relations

Easy

The relation $S$ in the set $R$ of real numbers,defined as $S = \{(a, b) : a < b^2\}$ is a . . . . . . relation.

GSEB 2021 All GSEB

A
reflexive
B
transitive
C
symmetric
D
not an equivalence

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Relation and Function

Subtopic

Types of Relations

Previous Year

GSEB 2021 Paper All GSEB years →

Let $M$ denote the set of all $3 \times 3$ non-singular matrices. Define the relation $R$ by $R = \{ (A,B) \in M \times M : AB = BA \}$. Then $R$ is-

View Solution

On $R$, the set of real numbers, a relation $\rho$ is defined as $a \rho b$ if and only if $1+a b > 0$. Then,

EasyWBJEE 2017

View Solution

Let $R$ and $S$ be two relations on a set $A$. Then which of the following is true?

Easy

View Solution

Show that the relation $R$ in the set $\{1, 2, 3\}$ given by $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)\}$ is reflexive but neither symmetric nor transitive.

Easy

View Solution

Let $A = \{1, 2, 3, 4, 5\}$. $A$ relation $R$ on $A$ is defined by $R = \{(x, y) | x, y \in A \text{ and } x < y\}$. Then $R$ is:

Easy

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The relation $S$ in the set $R$ of real numbers,defined as $S = \{(a, b) : a < b^2\}$ is a . . . . . . relation.

Similar Questions

Let $M$ denote the set of all $3 \times 3$ non-singular matrices. Define the relation $R$ by $R = \{ (A,B) \in M \times M : AB = BA \}$. Then $R$ is-

On $R$, the set of real numbers, a relation $\rho$ is defined as $a \rho b$ if and only if $1+a b > 0$. Then,

Let $R$ and $S$ be two relations on a set $A$. Then which of the following is true?

Show that the relation $R$ in the set $\{1, 2, 3\}$ given by $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)\}$ is reflexive but neither symmetric nor transitive.

Let $A = \{1, 2, 3, 4, 5\}$. $A$ relation $R$ on $A$ is defined by $R = \{(x, y) | x, y \in A \text{ and } x < y\}$. Then $R$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module