I have question what is the no. of equivalence and transitive relations on a set of cardinality n? my name is Siddhartha I am a student of Computer Science at IIT, Kharagpur(INDIA) Hi Siddhartha, The number of equivalence relations on a set of cardinality n is the same as the number of partitions of the set. These are counted by what we call Stirling numbers of the second kind  S(n,i) is the number of ways to partition an nset into i nonempty sets. S(n,i) may be obtained by an inclusionexclusion argument and then you need to sum these up over i = 1 to n. Penny
