What is the fundamental difference between a relation and a function?

1.	What is the fundamental difference between a relation and a function? Is every relation a function?
Answer» Suppose ‘f’ be the function and R be the relation defined from the set X to set Y. A domain of a relation R might be a subset of the set X, but the domain of the function f must be equal to X. This is because each element of the domain of a function must have an element associated with it, whereas this is not necessary for a relation. In the relation, one element of X might be associated with the one or more elements of Y, while it must be associated with the only one element of Y in a function. Hence, not every relation is a function. However, every function is necessarily a relation.

What is the fundamental difference between a relation and a function? Is every relation a function?

Answer»

Suppose ‘f’ be the function and R be the relation defined from the set X to set Y.

A domain of a relation R might be a subset of the set X, but the domain of the function f must be equal to X. This is because each element of the domain of a function must have an element associated with it, whereas this is not necessary for a relation.

In the relation, one element of X might be associated with the one or more elements of Y, while it must be associated with the only one element of Y in a function.

Hence, not every relation is a function. However, every function is necessarily a relation.

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