Is there a short cut to determine the number of equivalence relations on the set $\{1,2,3,4\}$? I mean I could do that manually but for a larger set it becomes annoying. Is there a general way to partition it?
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Yes there is, check Bell number.
It gives you a Recurrence relation for calculating number of equivalence relations on a set having $n$ elements.
Shobhit
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Yes thx. It is strange somehow. Using the Bell numbers I get for $n=4$ set $15$ different partitions...according to my solution there must be 18. – Mamba Jan 25 '15 at 19:41
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@mamba can u list the partitions u made, i'll try to correct u – Shobhit Jan 26 '15 at 03:25