Relations In Mathematics: Reflexive, Symmetric, Transitive And Equivalence Relations

relation

any set of ordered pairs

In mathematics, a relation is a set of ordered pairs that describes the relationship between elements in two sets. A relation is often represented as a graph or a table of values. In more formal terms, a relation is a subset of the Cartesian product of the two sets, meaning it only contains ordered pairs where the first element comes from one set and the second element comes from the other set.

There are several types of relations, including reflexive, symmetric, transitive, and equivalence relations. A reflexive relation is one where each element is related to itself (for example, the relation is equal to is reflexive). A symmetric relation is one where if (a,b) is in the relation, then (b,a) is also in the relation (for example, the relation is a sibling of is symmetric). A transitive relation is one where if (a,b) and (b,c) are in the relation, then (a,c) must also be in the relation (for example, the relation is taller than is transitive).

Equivalence relations are a type of relation that satisfy three properties: reflexivity, symmetry, and transitivity. Equivalence relations divide a set into distinct partitions, where elements in each partition are considered equivalent to each other, but not to elements in other partitions. Some examples of equivalence relations include is congruent to and is equivalent to.

More Answers: