Let $S$ be a set and $\{X_i\}$ be a partition of $S$. Show that $xRy$ if and only if $x, y$ are in the same part of the partition, defines an equivalence relation. What are the equivalence classes of this relation?

  • $\begingroup$ What is your question? $\endgroup$ – AnotherJohnDoe Sep 17 '18 at 3:56
  • $\begingroup$ I am uncertain how to prove this iff statement $\endgroup$ – david D Sep 17 '18 at 3:59
  • $\begingroup$ What have you tried as of yet? Can you guess what an equivalence relation on the partition might be? $\endgroup$ – AnotherJohnDoe Sep 17 '18 at 4:00
  • $\begingroup$ I know the equivalence classes of an equivalence relation form a partition. But I am not sure how can a equivalence relation on a partition? $\endgroup$ – david D Sep 17 '18 at 4:04
  • $\begingroup$ Let's try to guess - for the partition formed by an equivalence relation, what are the equivalence classes? $\endgroup$ – AnotherJohnDoe Sep 17 '18 at 4:05

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