Let R be a relation on a given nonempty set A. State the necessary and sufficient condition for R to be an equivalence relation on A.
The conditions for any equivalence relation are Transitivity, Symmetric and Reflexive.
Reflexive : For all elements $x\in A$, $xRx$. Therefore, this is a necessary condition.
Symmetric : If $aRb$, then $bRa$. Since this is conditional, it should be a sufficient condition.
Transitivity : If $aRb$ and $bRc$, then $aRc$. Since this is conditional, it should be a sufficient condition.
Am I correct?