can you explain me the difference between refflexive and irreflexive relation
and
can a relation on a set br 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?