Difference between Relation and Function


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Difference between Relation and Function

The difference between relations and functions are a bit confusing as they both are closely related to each other. To differentiate the relation and function, we need detailed knowledge and comprehension of relations and functions.

Definition of Relation and Function in Maths

Relation- In maths, the relation is defined as the collection of ordered pairs, which contains an object from one set to the other set. For instance, X and Y are the two sets, and ‘a’ is the object from set X and b is the object from set Y, then we can say that the objects are related to each other if the order pairs (a, b) is to be in relation.

Functions- The relation that defines the set of inputs to the set of outputs is called the functions. In function, each input in the set X has exactly one output in the set Y.

Note: All functions are relations but all relations are not functions.

Consider for an example Set X & Set Y are related in a manner that all the elements of Set X are related to exactly one element of Set Y or many elements of set X are related to one element of Set y. Thus, this type of relation is said to be a function.

Note that a function cannot Possess One-to-Many relation between the set X and Y.

What is the Difference Between Relations and Functions?

Differentiating Parameter Relations Functions
Definition A relation is a relationship between sets of values. Or, it is a subset of the Cartesian product A function is a relation in which there is only one output for each input.
Denotation A relation is denoted by “R” A function is denoted by “F” or “f”.
Example R = {(2, x), (9, y), (2, z)}

** It is not a function, as “2” is input for both x and z.

F = {(2, x), (9, y), (5, x)}
Note: Every relation is not a function. Every function is a relation.

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Frequently Asked Questions on Difference between Relation and Function

What is the definition of relation and function?

A relation shows the relationship between input and output and a function is a relation which derives one OUTPUT for each given INPUT

What is domain and range in function?

Domain is the set of all inputs and range is the set of all outputs.

What are the types of relation in Maths?

There are basically four types of relation: Reflexive, Symmetric, Transitive and Anti-Symmetric.

What are the types of functions in Maths?

There are various types of functions in Maths, such as:
One to one Function or Injective Function
Many to one function
Onto function or Surjective function
Polynomial function
Linear Function
Identical Function
Quadratic Function
Identity Function