Every equivalence relation on a set A partitions A into disjoint, non-empty subsets called equivalence classes, and conversely, every partition defines an equivalence relation. The equivalence class of element a is [a] = {x in A : xRa}. Properties: every element belongs to exactly one class, two classes are either identical or disjoint, and the union of all classes equals A. Example: "a ≡ b (mod n)" is an equivalence relation on integers, partitioning Z into n classes {[0], [1], ..., [n-1]}. The number of equivalence relations on a set of n elements is the Bell number B(n): B(1)=1, B(2)=2, B(3)=5, B(4)=15, B(5)=52. This is a common JEE counting problem.