# reflexive and irreflexive relation

• Aug 22nd 2013, 02:24 AM
annie12
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
• Aug 22nd 2013, 03:21 AM
Plato
Re: reflexive and irreflexive relation
Quote:

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?
• Aug 22nd 2013, 03:46 AM
annie12
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