# Thread: reflexive and irreflexive relation

1. ## reflexive and irreflexive relation

can you explain me the difference between refflexive and irreflexive relation
and
can a relation on a set br neither reflexive nor irreflexive

2. ## Re: reflexive and irreflexive relation

Originally Posted by annie12
can you explain me the difference between refflexive and irreflexive relation
and can a relation on a set be neither reflexive nor irreflexive
Consider $\displaystyle A=\{a,b,c\}$ and :
$\displaystyle \\\mathcal{R}_1=\{(a,a),(b,b),(c,c),(a,b),(b,c)\}, \\\mathcal{R}_2=\{(a,b),(b,c),(c,a)\},~\&\\ \mathcal{R}_3=\{(a,a),(c,c),(a,b),(b,c)\}$

The relation $\displaystyle \mathcal{R}_1$ is reflexive because each element is related to itself.

The relation $\displaystyle \mathcal{R}_2$ is irreflexive because no element is related to itself.

The relation $\displaystyle \mathcal{R}_3$ is neither reflexive nor irreflexive. WHY?

3. ## Re: reflexive and irreflexive relation

in R1 (a,b),(b,c) is not related to its self so how can u say it is reflexive
and in R3 (a,b)(b,c) is a part of irreflexive relation so how how it is nor irreflexive
please explain me the if i am right or wrong

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# reflexive and irreflexive

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