# 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. |

### Check out More Difference Between Articles:

Difference Between Rational And Irrational Numbers | Difference Between Fraction And Rational Number |

Difference Between Codomain And Range | Difference Between Natural And Whole Numbers |

## Frequently Asked Questions on Difference between Relation and Function

### What is the definition of relation and function?

### What is domain and range in function?

### What are the types of relation in Maths?

### What are the types of functions in Maths?

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