# Show that $xRy$ if and only if $x, y$ are in the same part of the partition defines an equivalence relation.

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?

• What is your question? – AnotherJohnDoe Sep 17 '18 at 3:56
• I am uncertain how to prove this iff statement – david D Sep 17 '18 at 3:59
• What have you tried as of yet? Can you guess what an equivalence relation on the partition might be? – AnotherJohnDoe Sep 17 '18 at 4:00
• 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？ – david D Sep 17 '18 at 4:04
• Let's try to guess - for the partition formed by an equivalence relation, what are the equivalence classes? – AnotherJohnDoe Sep 17 '18 at 4:05