# Describe difference between relation and function

A function is defined as the set of ordered pairs such as (x,y), which is used for showing the relationship between the input and output. Also, this explains that there is one output for every input. A relation is defined as ordered pairs such as (x,y) where the input can have more than one output.

### Comparison

• If the set (x,y) is in the collection of ordered pairs, x is from set A while y is from set B. Then we say x is related to y. A group of such sets is called a relation.
• In a function, exactly one x can be paired with some y., where x is from set B, and y is from set B.
• All functions are relations, but all relations are not functions. This is because one input can connect to only one output in a function and not more than one, while there is no such condition in a relation.
• The function does not have a one-many relationship, which means one object cannot pair up with many objects in a function.
• Many-one relation is valid in a function. Thus, many objects can be paired with the same object.