Difference between Relation and Function

The difference between relations and functions are a bit confusing as they both are closely related to each other. One needs to have a clear knowledge an understanding of relations and functions to be able to differentiate them. Here, the differences between them are provided below in a tabular form.

Relation- Two or more sets can be related to each other by any means. Consider for an example two sets A and B having m and n elements respectively, we can have a relation with any ordered pair which shows a relation between the two sets.

Functions- A functions can have the same Range mapped as that of in Relation, such that a set of inputs is related with exactly one output.

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

It is to be noted that a function cannot have One to Many Relation between the set A and B.

Relations and Functions Differences:

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 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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