Equivalence Relations and Bell Numbers

It is well known that for a given finite set, an equivalence relation induces a partition of the set. This paper addresses the question of counting the number of equivalence relations that can be defined on a given finite set. Interestingly enough the answer lies in special class of numbers called “Bell Numbers”. In this paper, we witness this amusing connection obtained through another special class of numbers called Stirling’s numbers of second kind. Some of the basic properties of Stirling’s numbers and Bell numbers were proved.