An integer m is said to be related to another integer n if m is a multiple of n . Then relation is

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1.Relation and Function

easy

An integer $m$ is said to be related to another integer $n$ if $m$ is a multiple of $n$. Then the relation is

Reflexive and symmetric

Reflexive and transitive

Symmetric and transitive

Equivalence relation

Solution

(b) For any integer $n$, we have $n|n \Rightarrow n\,R\,n$

So, $n\,R\,n$ for all $n \in Z \Rightarrow R$ is reflexive

Now $2|6$ but $6+2,==> (2,6)$$ \in R$ but $(6, 2)$ $\not \in R$

So, $R$ is not symmetric.

Let $(m,n) \in R$ and $(n,p) \in R$.

Then $\left. {\begin{array}{*{20}{c}}
{(m,n) \in R \Rightarrow m|n} \\
{(n,p) \in R \Rightarrow n|p}
\end{array}} \right] \Rightarrow m|p \Rightarrow (m,p) \in R$

So, $R$ is transitive.

Hence, $R$ is reflexive and transitive but it is not symmetric.

Standard 12

Mathematics

Let $r$ be a relation from $R$ (Set of real number) to $R$ defined by $r$ = $\left\{ {\left( {x,y} \right)\,|\,x,\,y\, \in \,R} \right.$ and $xy$ is an irrational number $\}$ , then relation $r$ is

normal

Let $\mathrm{T}$ be the set of all triangles in a plane with $\mathrm{R}$ a relation in $\mathrm{T}$ given by $\mathrm{R} =\left\{\left( \mathrm{T} _{1}, \mathrm{T} _{2}\right): \mathrm{T} _{1}\right.$ is congruent to $\left. \mathrm{T} _{2}\right\}$ . Show that $\mathrm{R}$ is an equivalence relation.

easy

If $R_{1}$ and $R_{2}$ are equivalence relations in a set $A$, show that $R_{1} \cap R_{2}$ is also an equivalence relation.

easy

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

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

easy

An integer $m$ is said to be related to another integer $n$ if $m$ is a multiple of $n$. Then the relation is

Solution

Similar Questions

Let $r$ be a relation from $R$ (Set of real number) to $R$ defined by $r$ = $\left\{ {\left( {x,y} \right)\,|\,x,\,y\, \in \,R} \right.$ and $xy$ is an irrational number $\}$ , then relation $r$ is

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