https://gateoverflow.in/54949/how-many-equivalence-classes-can-be-made-form-1-2-3 https://en.wikipedia.org/wiki/Bell_number
On the wiki page under the section for set partitions it says that for a set {a,b,c} there are 5 set partitions, and in the top link it says that there are 5 equivalence relations, how are these related?