Let A={2,3,6,8,9,11} and B={1,4,5,10,15} Let mathrm{R} be a relation on mathrm{A} × mathrm{B} defin

English

Gujarati

Hindi

1.Relation and Function

hard

Let $A=\{2,3,6,8,9,11\}$ and $B=\{1,4,5,10,15\}$

Let $\mathrm{R}$ be a relation on $\mathrm{A} \times \mathrm{B}$ define by $(\mathrm{a}, \mathrm{b}) \mathrm{R}(\mathrm{c}, \mathrm{d})$ if and only if $3 \mathrm{ad}-7 \mathrm{bc}$ is an even integer. Then the relation $\mathrm{R}$ is

reflexive but not symmetric.

transitive but not symmetric.

reflexive and symmetric but not transitive.

an equivalence relation.

(JEE MAIN-2024)

Solution

$ \mathrm{A}=\{2,3,6,8,9,11\} \quad(\mathrm{a}, \mathrm{b}) \mathrm{R}(\mathrm{c}, \mathrm{d}) $

$ \mathrm{B}=\{1,4,5,10,15\} \quad 3 \mathrm{ad}-7 \mathrm{bc} $

$ \text { Reflexive : }(\mathrm{a}, \mathrm{b}) \mathrm{R}(\mathrm{a}, \mathrm{b})$

$\Rightarrow 3 \mathrm{ab}-7 \mathrm{ba}=-4 \mathrm{ab}$ always even so it is reflexive.

Symmetric : If $3 \mathrm{ad}-7 \mathrm{bc}=$ Even

Case $-I$ : odd odd

Case $-II$ : even even

$(\mathrm{c}, \mathrm{d}) \mathrm{R}(\mathrm{a}, \mathrm{b}) \Rightarrow 3 \mathrm{bc}-3 \mathrm{ab}$

Case $-I$ : odd odd

Case $-II$ : even even

so symmetric relation

Transitive :

Set $(3,4) R(6,4)$ Satisfy relation

Set $(6,4) R(3,1)$ Satisfy relation

but $(3,4) R(3,1)$ does not satisfy relation so not transitive.

Standard 12

Mathematics

Let $A=\{1,2,3\} .$ Then show that the number of relations containing $(1,2) $ and $(2,3)$ which are reflexive and transitive but not symmetric is four.

medium

If $R$ is a relation from a set $A$ to a set $B$ and $S$ is a relation from $B$ to a set $C$, then the relation $SoR$

normal

Let $R$ be a relation from $A = \{2,3,4,5\}$ to $B = \{3,6,7,10\}$ defined by $R = \{(a,b) |$ $a$ divides $b, a \in A, b \in B\}$, then number of elements in $R^{-1}$ will be-

normal

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

Relation $\mathrm{R}$ in the set $\mathrm{A}=\{1,2,3,4,5,6\}$ as $\mathrm{R} =\{(\mathrm{x}, \mathrm{y}): \mathrm{y}$ is divisible by $\mathrm{x}\}$

medium

If $R$ is an equivalence relation on a Set $A$, then $R^{-1}$ is not :-

normal

Let $A=\{2,3,6,8,9,11\}$ and $B=\{1,4,5,10,15\}$ Let $\mathrm{R}$ be a relation on $\mathrm{A} \times \mathrm{B}$ define by $(\mathrm{a}, \mathrm{b}) \mathrm{R}(\mathrm{c}, \mathrm{d})$ if and only if $3 \mathrm{ad}-7 \mathrm{bc}$ is an even integer. Then the relation $\mathrm{R}$ is

Solution

Similar Questions

Let $A=\{1,2,3\} .$ Then show that the number of relations containing $(1,2) $ and $(2,3)$ which are reflexive and transitive but not symmetric is four.

If $R$ is a relation from a set $A$ to a set $B$ and $S$ is a relation from $B$ to a set $C$, then the relation $SoR$

Let $R$ be a relation from $A = \{2,3,4,5\}$ to $B = \{3,6,7,10\}$ defined by $R = \{(a,b) |$ $a$ divides $b, a \in A, b \in B\}$, then number of elements in $R^{-1}$ will be-

Determine whether each of the following relations are reflexive, symmetric and transitive: Relation $\mathrm{R}$ in the set $\mathrm{A}=\{1,2,3,4,5,6\}$ as $\mathrm{R} =\{(\mathrm{x}, \mathrm{y}): \mathrm{y}$ is divisible by $\mathrm{x}\}$

If $R$ is an equivalence relation on a Set $A$, then $R^{-1}$ is not :-

Start a Free Trial Now

Let $A=\{2,3,6,8,9,11\}$ and $B=\{1,4,5,10,15\}$

Let $\mathrm{R}$ be a relation on $\mathrm{A} \times \mathrm{B}$ define by $(\mathrm{a}, \mathrm{b}) \mathrm{R}(\mathrm{c}, \mathrm{d})$ if and only if $3 \mathrm{ad}-7 \mathrm{bc}$ is an even integer. Then the relation $\mathrm{R}$ is

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

Relation $\mathrm{R}$ in the set $\mathrm{A}=\{1,2,3,4,5,6\}$ as $\mathrm{R} =\{(\mathrm{x}, \mathrm{y}): \mathrm{y}$ is divisible by $\mathrm{x}\}$