A relation R from set A to set B is a subset of the Cartesian product A x B. A relation on a set A is a subset of A x A. The four key properties: Reflexive — (a,a) in R for every a in A; Symmetric — (a,b) in R implies (b,a) in R; Antisymmetric — (a,b) and (b,a) in R implies a = b; Transitive — (a,b) and (b,c) in R implies (a,c) in R. An equivalence relation is reflexive, symmetric, and transitive — it partitions the set into equivalence classes. A partial order is reflexive, antisymmetric, and transitive (like <= on integers). The number of relations on an n-element set is 2^($n^2$). The number of reflexive relations is 2^($n^{2-n}$). Counting equivalence relations gives the Bell numbers.