Learn Class 12 Math - Relations and Functions

The relation refers to a relationship between the different sets of elements of the values with the complete pair of sets. These elements set in their first set are known as Domains. Further, which is related to the whole element set called the Range. Whereas Functions are known as relations are the complete set of the output.

Relation

Mainly, the relation is the main output between the output and input.

Types of Relation

Relations are of many types. The list of the different kinds of relationships is below:

• Empty relations: When the set of A does not relate to any element of X, then it is known as empty relations.
• Reflexive relations: When every set element is related to itself, then it is a reflexive relation.
• Identity Relations: When the set elements are related to itself only, then it is known as identity relations.

Functions:

Consider X and Y as two sets that are not empty. f : X → Y is the mapping or function between X and Y by which each element x ∈ X corresponds to an element y ∈ Y. Domain of X is composed of elements of X and the codomain of X is composed of elements of Y. Range of X is a subset of Y that represents the image of the element of X.

Types of Functions

Functions are of different types.

• Injective functions: The injective function is the f function, i.e., f: A →B. For the element A, B is a distinct function.
• Many to one function: It is a type of function that includes two or more map elements.
• Surjective function: In every element of set B, a preimage element is set A, known as surjective functions.