can you explain me the difference between refflexive and irreflexive relation

and

can a relation on a set br neither reflexive nor irreflexive

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- Aug 22nd 2013, 02:24 AMannie12reflexive 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 - Aug 22nd 2013, 03:21 AMPlatoRe: reflexive and irreflexive relation
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? - Aug 22nd 2013, 03:46 AMannie12Re: 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