Shortcut for determining equivalence relations?

Question

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?

Answer 1

Yes there is, check Bell number.

It gives you a Recurrence relation for calculating number of equivalence relations on a set having $n$ elements.