Let $R$ be the relation in the set $\{1,2,3,4\}$ given by $R =\{(1,2),\,(2,2),\,(1,1),\,(4,4)$ $(1,3),\,(3,3),\,(3,2)\}$. Choose the correct answer.
Let $R$ be the relation in the set $\{1,2,3,4\}$ given by $R =\{(1,2),\,(2,2),\,(1,1),\,(4,4)$ $(1,3),\,(3,3),\,(3,2)\}$. Choose the correct answer.
$R=\{(1,2),\,(2,2),\,(1,1),\,(4,4),\,(1,3),\,(3,3),\,(3,2)\}$
It is seen that $(a, \,a) \in R,$ for every $a \in\{1,\,2,\,3,\,4\}$
$\therefore R$ is reflexive.
It is seen that $(1,\,2) \in R ,$ but $(2,\,1)\notin R$
$\therefore R$ is not symmetric.
Also, it is observed that $(a, \,b),\,(b, \,c) \in R \Rightarrow(a,\, c) \in R$ for all $a, \,b, \,c \in\{1,\,2,\,3,\,4\}$
$\therefore R$ is transitive.
Hence, $R$ is reflexive and transitive but not symmetric.
The correct answer is $B$.
Similar Questions
The probability that a relation $R$ from $\{ x , y \}$ to $\{ x , y \}$ is both symmetric and transitive, is equal to
The probability that a relation $R$ from $\{ x , y \}$ to $\{ x , y \}$ is both symmetric and transitive, is equal to
- [JEE MAIN 2022]
Let $L$ be the set of all straight lines in the Euclidean plane. Two lines ${l_1}$ and ${l_2}$ are said to be related by the relation $R$ iff ${l_1}$ is parallel to ${l_2}$. Then the relation $R$ is
Let $L$ be the set of all straight lines in the Euclidean plane. Two lines ${l_1}$ and ${l_2}$ are said to be related by the relation $R$ iff ${l_1}$ is parallel to ${l_2}$. Then the relation $R$ is
Let $R$ be a relation on a set $A$ such that $R = {R^{ - 1}}$, then $R$ is
Let $R$ be a relation on a set $A$ such that $R = {R^{ - 1}}$, then $R$ is
Let $A=\{1,2,3, \ldots 20\}$. Let $R_1$ and $R_2$ two relation on $\mathrm{A}$ such that $\mathrm{R}_1=\{(\mathrm{a}, \mathrm{b}): \mathrm{b}$ is divisible by $\mathrm{a}\}$ $\mathrm{R}_2=\{(\mathrm{a}, \mathrm{b}): \mathrm{a}$ is an integral multiple of $\mathrm{b}\}$. Then, number of elements in $R_1-R_2$ is equal to_____.
Let $A=\{1,2,3, \ldots 20\}$. Let $R_1$ and $R_2$ two relation on $\mathrm{A}$ such that $\mathrm{R}_1=\{(\mathrm{a}, \mathrm{b}): \mathrm{b}$ is divisible by $\mathrm{a}\}$ $\mathrm{R}_2=\{(\mathrm{a}, \mathrm{b}): \mathrm{a}$ is an integral multiple of $\mathrm{b}\}$. Then, number of elements in $R_1-R_2$ is equal to_____.
- [JEE MAIN 2024]
Let a relation $R$ on $\mathbb{N} \times \mathbb{N}$ be defined as : $\left(\mathrm{x}_1, \mathrm{y}_1\right) \mathrm{R}\left(\mathrm{x}_2, \mathrm{y}_2\right)$ if and only if $\mathrm{x}_1 \leq \mathrm{x}_2$ or $\mathrm{y}_1 \leq \mathrm{y}_2$
Consider the two statements :
($I$) $\mathrm{R}$ is reflexive but not symmetric.
($II$) $\mathrm{R}$ is transitive
Then which one of the following is true?
Let a relation $R$ on $\mathbb{N} \times \mathbb{N}$ be defined as : $\left(\mathrm{x}_1, \mathrm{y}_1\right) \mathrm{R}\left(\mathrm{x}_2, \mathrm{y}_2\right)$ if and only if $\mathrm{x}_1 \leq \mathrm{x}_2$ or $\mathrm{y}_1 \leq \mathrm{y}_2$
Consider the two statements :
($I$) $\mathrm{R}$ is reflexive but not symmetric.
($II$) $\mathrm{R}$ is transitive
Then which one of the following is true?
- [JEE MAIN 2024]