Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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 ...

share|cite|improve this question
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 $x\in X\setminus A$."

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.