I have to give an mere example where SR is not equal to RS.
I have tried a couple of numerical examples but am not able to figure any out.
2026-03-31 18:25:44.1774981544
Give an example of a set A with equivalence relations R and S for which S∘R ≠ R∘S
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Somehow I've never come across relation composition before!
Anyway, this should work. Let $A = \{a, b, c\}$. Let $R$ equate $a, b$ and leave $c$ alone. Let $S$ equate $b, c$ and leave $a$ alone.
Then $aRSc$ but we don't have $aSRc$.
Let me know if I misunderstood the definition and I'll edit or delete my post.