Let $A=\{a,b,c,d,e\}$. Suppose $R$ is an equivalence relation on $A$. Suppose also that $aRd$ and $bRc$, $eRa$ and $cRe$. How many equivalence classes does $R$ have?
My thoughts: (Not sure if I have the right idea...)
UPDATED/EDITED
Since $R$ is an equivalence relation on $A$ and $aRd$, $bRc$, $eRa$, and $cRe$, then
$R=\{(a,d),(d,a),(a,a),(d,d),(b,c),(c,b),(c,c),\\ (b,b),(e,a),(a,e),(e,e),(c,e),(e,c)\}$ (Did I miss any?)
So $R$ has $1$ equivalence class:
- $[a]=[b]=[c]=[d]=[e]=\{a,b,c,d,e\}$