Number of equivalence relations = number of partitions
Number of partitions can be given by using Bell Number.
For smaller numbers we can construct Bell's triangle by taking B0=B1=1.
Than by taking the last number of the previous row as the starting number in the next row, adding the numbers column wise and writing it next.
eg:
1
1 2
2 3 5
5 7 10 15
B0 = 1
B1= 1
B2= 2
B3= 5
B4= 15