Given the set $A=\{1,2,3\}$
How many different binary equivalence relations can be formed?
Can I list all of them?
Furthermore, how will this answer change as I add more elements to the set?
2026-03-30 15:10:10.1774883410
How many binary equivalences are there on a $3$ element set?
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Remember that every equivalence relation on a set defines a partition, and vice versa. So look at ways to break up $\{1,2,3\}$ into nonempty pieces. $\{\{1\},\{2,3\}\}$ is one. But then you have $\{\{2\},\{1,3\}\}$ and $\{\{3\},\{1,2\}\}$...