I need help understanding the quotient of an equivalence relation

Question

I understand it in theory,but not in practice So here is the exampl

1. LetA={a,b,c,d,e,f}
2. G,H be equivalence relation in A

3.G=$1_a$ $\cup$ {(a,b),(b,a),(b,c),(c,b),(a,c), (c,a),(d,e),(e,d)}

H=$1_a$ $\cup$ {(b,c),(c,b)}

Find A/G

Here is my guess

A/G=G

Any help would be mighty appreciated to figure out how to do this

Answer 1

$a$ is related to $b$ under the equivalence relation given by $G$, $b$ is related to $c$, so $a$ is related to $b$ and by transitivity to $c$, hence the equivalence class of $a$ is the subset $\{a,b,c\}$ of $A$. Then $d$ is related to $e$ and $f$ is related to $f$ itself. Hence the set of distinct equivalence classes of $A$ modulo $G$ is given by $\{a,b,c\}, \{d,e\}$, and $\{f\}$.