Let A = {1, 2, 3, 4} and R be a relation in A given by R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2),

English

Gujarati

Hindi

1.Relation and Function

easy

Let $A = \{1, 2, 3, 4\}$ and $R$ be a relation in $A$ given by $R = \{(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (3, 1), (1, 3)\}$. Then $R$ is

A

Reflexive

B

Transitive

C

An equivalence relation

D

none of these

Solution

(a) $(1, 1)(2, 2)(3, 3)(4, 4) \in R$

$\therefore$ $R$ is reflexive.

$\therefore $ $(1, 2) (3, 1)$$ \in R$ and also $(2, 1)(1, 3) $$ \in R$

Hence, $R$ is symmetric. But clearly $R$ is not transitive.

Standard 12

Mathematics

Share

Similar Questions

Give an example of a relation. Which is Reflexive and symmetric but not transitive.

easy

The relation "is subset of" on the power set $P(A)$ of a set $A$ is

easy

Determine whether each of the following relations are reflexive, symmetric and transitive:

Relation $R$ in the set $A$ of human beings in a town at a particular time given by

$R =\{(x, y): x $ is father of $y\}$

medium

The relation $R =\{( x , y ): x , y \in z$ and $x + y$ is even $\}$ is :

medium

(JEE MAIN-2025)

The number of relations $R$ from an $m$-element set $A$ to an $n$-element set $B$ satisfying the condition$\left(a, b_1\right) \in R,\left(a, b_2\right) \in R \Rightarrow b_1=b_2$ for $a \in A, b_1, b_2 \in B$ is

normal

(KVPY-2009)