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If $X = \{1,2,3\}$ then a partition of $C$ of $X$ could be $\{\{1\},\{2,3\}\}$. Correct?

Does this partition equal the relation $\{(1,1),(2,3),(2,2),(3,3),(3,2)\}$ is this an equivalence relation? Does the set of equivalence classes $= \{\{1\},\{2,3\}\}$?

Sorry I just trying to understand the relationship between equivalence relations and partitions.

Thanks in advance...

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Partitions and equivalence relations on a set $X$ determine each other, but they are not equal.
Other than that, your example is correct.

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  • 1
    $\begingroup$ Thank you, I'm beginning to understand it now! $\endgroup$ – Paul Aug 14 '18 at 11:16
  • $\begingroup$ Does every set induce an equivalence relation? $\endgroup$ – Paul Aug 14 '18 at 11:17
  • $\begingroup$ How do you mean it? $\endgroup$ – Berci Aug 14 '18 at 21:48

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