Let L denote set of all straight lines in a plane. Let a relation R be defined by α Rβ Leftrightar

English

Gujarati

Hindi

1.Relation and Function

easy

Let $L$ denote the set of all straight lines in a plane. Let a relation $R$ be defined by $\alpha R\beta \Leftrightarrow \alpha \bot \beta ,\,\alpha ,\,\beta \in L$. Then $R$ is

A

Reflexive

B

Symmetric

C

Transitive

D

None of these

Solution

(b) Here $\alpha R\beta \Leftrightarrow \alpha \bot \beta $

$\therefore \alpha \, \bot \,\beta \Leftrightarrow \beta \, \bot \,\alpha $

Hence, $R$ is symmetric.

Standard 12

Mathematics

Share

Similar Questions

Let $R$ and $S$ be two relations on a set $A$. Then

normal

Let $A=\{2,3,6,7\}$ and $B=\{4,5,6,8\}$. Let $R$ be a relation defined on A $\times$ B by $\left(a_1, b_1\right) R\left(a_2, b_2\right)$ is and only if $a_1+a_2=b_1+b_2$. Then the number of elements in $\mathrm{R}$ is ………..

hard

(JEE MAIN-2024)

Show that the relation $R$ in the set $A=\{1,2,3,4,5\}$ given by $R =\{(a, b):|a-b|$ is even $\},$ is an equivalence relation. Show that all the elements of $\{1,3,5\}$ are related to each other and all the elements of $ \{2,4\}$ are

medium

Let $X = R \times R$. Define a relation $R$ on $X$ as: $\left(a_1, b_1\right) R\left(a_2, b_2\right) \Leftrightarrow b_1=b_2 .$ Statement-$I: R$ is an equivalence relation. Statement$-II$: For some $( a , b ) \in X$, the set $S=\{(x, y) \in X:(x, y) R(a, b)\}$ represents a line parallel to $y = x$. In the light of the above statements, choose the correct answer from the options given below:

medium

(JEE MAIN-2025)

Let $H$ be the set of all houses in a village where each house is faced in one of the directions, East, West, North, South. Let $R = \{ (x,y)|(x,y) \in H \times H$ and $x, y$ are faced in same direction $\}$ . Then the relation $' R '$ is

normal