equivalence relation and quotient set, Given $A = \{0,1,2,3,4,5\}$ Given $A = \{0,1,2,3,4,5\}$, Write the appropriate equivalence relation of this quotient set:
$$A/_R = \{\{1,2\},\{3\},\{4,0,5\}\}$$
Well, if it was to compute $$A/_R = \{\{0\},\{1\},\{2\},\{3\},\{4\},\{5\}\}$$ I believe it would be simpler, something like:
$[0]_r = \{0\}$, $[1]_r = \{1\}$ , $[2]_r = \{2\}$ , $[3]_r = \{3\}$ , $[4]_r = \{4\}$, $[5]_r = \{5\}$
How do I compute if there is something like $\{1,2\}$? Thanks on advance!

You can find the ordered pairs belonging to $R$ on base of:
$$R=\{\langle x,y\rangle\mid x,y\in\{1,2\}\vee x,y\in\{3\}\vee x,y\in\{4,0,5\}\}$$
That leads to something like:
$$R=\{\langle1,1\rangle,\langle1,2\rangle,\langle2,1\rangle,\langle2,2\rangle,\langle3,3\rangle,\dots\}$$
There will be $2^2+1^2+3^2=14$ pairs that belong to $R$.
