We need to apply Bell's no. to find the no. of equivalence relations on set of n elements.
The Bell's no. is expressed as:
Where S(n,k) is the total no. of partitions of n elements into k sets. It is known as Strirling's number of 2nd kind.
3rd Bell no. is 5. Shortcut is described in the link attached below (geeksforgeeks).
For more info :