Relaatiatermit

Relaatiatermit, or relation terms, are the standard vocabulary used to describe mathematical relations. In set theory and discrete mathematics, a relation R between sets A and B is a subset of the Cartesian product A × B. The relation can be described by listing the ordered pairs, by a graph, or by a matrix.

Core terms include domain (the set of elements that can appear as the first component), codomain (the target set), and image or range (the set of second components actually related to some element). A special kind of relation is a function, which relates each element of A to exactly one element of B. The inverse relation and the composition of relations are fundamental operations.

Relational properties classify relations: reflexive, irreflexive, symmetric, antisymmetric, asymmetric, and transitive. An equivalence relation is reflexive, symmetric, and transitive; a partial order is reflexive, antisymmetric, and transitive; a total order is a partial order in which every pair is comparable. Other terms include relation composition, closure, and converse.

Representation and notation: relations can be depicted as directed graphs, with vertices from A ∪ B and a directed edge from a to b if a R b; relation matrices or adjacency matrices can encode the same information. In education, relaatiatermit form the basis for understanding more advanced topics such as database relations and graph theory.