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...


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

  • 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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