Yesterday on my Abstract Algebra course, we were having a problem with equivalence relations. We had a given set: $A = \{a, b, c\}$
We found all the partitions of $A$, and one of them was: $P = \{ \{a\} , \{b, c\} \}$
Then we built an equivalence relation $S$ from this partition, where two elements are in equivalence relation if $a$ and $b$ belong to the same cell.
So the relation of equivalence is: $S = \{ (a,a) , (b,b) , (c,c) , (b,c) , (c,b) \}$
After this the professor, without explaining anything wrote:
The class of equivalence of $(b,c)$: $[(b,c)] = \{ (b,c) , (c,b) \}$
So can anyone explain this last line? Because I don't understand it.