What is Relation?
A relation is a collection of ordered pairs, pairing elements from distinct sets. These pairs signify a relationship between the elements, without prescribing a definite output for each input. Relations can exhibit various properties, influencing how elements interact across sets, forming the basis of mathematical analysis and modeling.
- Domain: Set of all input values in the relation.
- Codomain: Set of all possible output values.
- Range: Set of all actual output values obtained from the relation.
- Properties: Includes reflexivity, symmetry, transitivity, etc., influencing its behavior and characteristics.
Difference between Relation and Function
Relation defines how elements of one set relate to elements of another set whereas a Function is a special type of relation in which each element in the domain (input) is related to exactly one element in the codomain (output).
This article explores relations and functions, highlighting their definitions, properties, differences, and applications in mathematics.
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