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, detailed knowledge and comprehension of relations and functions may required. 

Relations: 

• A relation is a relationship between sets of values. Or, it is a subset of the Cartesian product
• A relation is denoted by “R”
• R = {(2, x), (9, y), (2, z)}
• ** It is not a function, as “2” is input for both x and z.
• Every relation is not a function.

Function: 

• A function is a relation in which there is only one output for each input.
• A function is denoted by “F” or “f”.
• Example: F = {(2, x), (9, y), (5, x)}
• Every function is a relation.