Let A={-4,-3,-2,0,1,3,4} and R ={( a , b ) ∈ A × A : b =| a | or left.b ^2= a +1right} be a relat

English

Gujarati

Hindi

1.Relation and Function

medium

Let $A=\{-4,-3,-2,0,1,3,4\}$ and $R =\{( a , b ) \in A$ $\times A : b =| a |$ or $\left.b ^2= a +1\right\}$ be a relation on $A$. Then the minimum number of elements, that must be added to the relation $R$ so that it becomes reflexive and symmetric, is $........$.

A

$5$

B

$7$

C

$6$

D

$4$

(JEE MAIN-2023)

Solution

$R=[(-4,4),(-3,3),(3,-2),(0,1),(0,0),(1,1)$, $(4,4),(3,3)\}$

For reflexive, add $\Rightarrow(-2,-2),(-4,-4),(-3,-3)$

For symmetric, add $\Rightarrow(4,-4),(3,-3),(-2,3),(1,0)$

Standard 12

Mathematics

Share

Similar Questions

Let $R = \{ (3,\,3),\;(6,\;6),\;(9,\,9),\;(12,\,12),\;(6,\,12),\;(3,\,9),(3,\,12),\,(3,\,6)\} $ be a relation on the set $A = \{ 3,\,6,\,9,\,12\} $. The relation is

medium

(AIEEE-2005)

In order that a relation $R$ defined on a non-empty set $A$ is an equivalence relation, it is sufficient, if $R$

normal

Let $L$ be the set of all lines in $XY$ plane and $R$ be the relation in $L$ defined as $R =\{\left( L _{1}, L _{2}\right): L _{1} $ is parallel to $L _{2}\} .$ Show that $R$ is an equivalence relation. Find the set of all lines related to the line $y=2 x+4$

medium

Let $A =\{2,3,4\}$ and $B =\{8,9,12\}$. Then the number of elements in the relation $R=\left\{\left(\left(a_1, b_1\right),\left(a_2, b_2\right)\right) \in(A \times B, A \times B): a_1\right.$ divides $b_2$ and $a_2$ divides $\left.b_1\right\}$ is:

medium

(JEE MAIN-2023)

Let $X$ be a family of sets and $R$ be a relation on $X$ defined by $‘A$ is disjoint from $B’$. Then $R$ is

medium