relation

Relation is a connection or association between two or more entities. In everyday language it denotes how things are connected or how they affect each other. In mathematics and computer science, a relation formalizes the idea of relating elements from one set to elements of another (or the same) set. A binary relation on a set A is a subset of A×A; more generally a relation from A to B is a subset of A×B. An element a in A is related to an element b in B if the pair (a,b) belongs to the relation.

Common properties include reflexivity, symmetry, and transitivity. A relation is reflexive if every element relates to itself; symmetric if the relation is mutual; transitive if a relates to b and b relates to c implies a relates to c. Equivalence relations are reflexive, symmetric, and transitive, and they partition the set into equivalence classes. Partial orders are reflexive, antisymmetric, and transitive, providing a notion of ordering without requiring total comparability.

In databases and logic, a relation is often viewed as a table: rows are tuples, columns are attributes; relational databases use operations such as selection, projection, join, and other relational algebra operations to manipulate relations.

In social science, relation covers interpersonal relationships, kinship, and other connections between individuals or groups, including familial, professional, and social ties. The study of relations examines how connections influence behavior, structure, and information flow.

Thus, “relation” spans abstract formalities to concrete social connections, serving as a foundational concept across disciplines.