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Let $X$ be a set and $A \subset X$ a subset. What equivalence relation on $X$ would give rise to the equivalence classes $A$ and $\{x\}$ for $x \in X \setminus A$. I'm unsure how to formulate the equivalence relation $x \sim y$ if ...

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up vote 2 down vote accepted


$x=y$, or, $x$ and $y$ are in $A$.

It could be clarified that you mean $A$ along with all of the singleton subsets of $X\setminus A$ (as opposed to choosing one particular $x$). For example, you might add a word: "equivalence classes $A$ and all $\{x\}$ for $x\in X\setminus A$."

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