Describe Difference Between Relation and Function

Question: Describe difference between relation and function

Relations and functions are one of the most critical topics of algebra. A relation is just a collection of ordered pairs. A function is also a relation but with one more extra rule.

Answer: Relations are a group of ordered pairs from one set of objects to other set of objects while functions are relations that connect one set of inputs to other set of outputs. So all functions are relations while are relations are not functions.

Let's compare relations and functions


From definition, relations and functions seem to be quite similar but actually there is a major difference between them.

  • If the set (x,y) is in collection of ordered pairs, where 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 in a function one input can connect to only one output and not more than one, while there is no such condition in a relation.

  • It can be said that function does not have one-many relationship, means one object cannot pair up with many objects in a function. 

  • Many-one relation is valid in a function. Many different objects can be paired with a same object.

Thus, we have seen the differences between relations and functions