Let $R$ and $S$ be equivalence relations on X so that $X/R$=$X/S$, prove that $R=S$ how can I solve this problem?
2026-04-07 06:57:49.1775545069
equivalence relation and quotient set problem
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HINT: Suppose that $\langle x,y\rangle\in R$; then $[x]_R=[y]_R$, where $[x]_R\in X/R$ is the $R$-equivalence class of $x$. By hypothesis $[x]_R=[x]_S$ and $[y]_R=[y]_S$. Can you finish it from here?