We need to apply Bell's no. to find the no. of equivalence relations on set of n elements.

The $n^{th}$ Bell's no. is expressed as:

$\sum_{k=0}^{n} S(n,k)$

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).

https://www.geeksforgeeks.org/bell-numbers-number-of-ways-to-partition-a-set/

https://brilliant.org/wiki/distinct-objects-into-identical-bins/