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Question

Let $S = \{1, 2, 3, 4\}$.

How many equivalence relation are there and describe them?

I know that 1~2 and 2~3. I also know that there are 2 equivalence relation but how do I prove that and describe them properly.

Community
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Zaynab Jamil
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  • $=$ is an equivalence relation. And you have the trivial "everything is related to everything" relation. That's 2. However, there are more. – Arthur Oct 25 '19 at 14:51

1 Answers1

4

The equivalence relations correspond to the partitions of the set and are counted by the Bell numbers.

RobPratt
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