Relations and equivalence relations

In real life, relations and function provide a link between two entities. In our daily lives, we encounter a variety of patterns and connections that explain relationships, such as the relationship between a parent and a son, brother, and sister, and so on. In mathematics, we encounter a variety of number relationships, such as x […]

Equivalence Relation Definition A binary relation is reflexive, symmetric, and transitive and is defined on a set X. The relation cannot be an equivalence relation if any of the three conditions—reflexive, symmetric, and transitive—are not met. The equivalence relation separates the set into distinct equivalence classes. If and only if two elements of the set

An ordered pair is, as its name suggests, a pair of components that have distinct significance for the order in which they are positioned inside a structure. In the field of coordinate geometry, ordered pairs are most frequently utilised to represent a point on a coordinate plane. In addition to this, we may use them

An equivalence relation in mathematics is a type of binary relation that needs to be transitive, symmetric, and reflexive. The “equal to (=)” relation is a well-known illustration of an equivalence relation. In other words, if two items of the given set are members of the same equivalence class, then they are equal to one

In mathematics, relations are used to describe the relationship between the elements of two sets. They aid in the mapping of elements from one set (the domain) to elements from another set (the range), resulting in ordered pairs of the type (input, output). Functions are also particular forms of relations that can be employed to