# How many equivalence relations are there on the set $\{1,2,3\}$?

How would I do this?

Do I separate it into partitions first? or do I order it by $(1,1)(1,2)(1,3)(2,1)$... etc.

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There's a one-to-one correspondence between equivalence relations and partitions, so you can certainly do it by carefully writing down all the ways to partition $\lbrace1,2,3\rbrace$ into subsets.