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Maths Notes for Exams: Relations and Functions | Definition & Examples

Empty Relation:

The relation R in a set A is said to be empty if no element of A is connected to another element of A.

Example:

Universal Relation:

A relation R in a set A is said to be a universal relation if each element of A is connected to every other element of A.

Example

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Identity Relation:

Every element of a set is only related to itself in an identity relation.

Example:

Inverse Relation:

When a set contains items that are inverse pairs of another set, it is said to have an inverse relation.

Example:

Reflexive Relation:

If (a, a) R, for every a > A, a relation R in a set A is considered reflexive.

Symmetric Relation:

A relation R in set A is called Symmetric

Transitive Relation:

A relation R is set A is called Transitive.

If a relation R in a set A is reflexive, symmetric, and transitive, then it is an equivalence relation.

Equivalence Relation:

Types of functions in terms of relations.

One-to-one function or Injective function:

If there is a unique element of Q for each element of P, then the function f: P to Q is said to be one-to-one.

Many to one function:

A function that maps two or more elements of P to the same element of set Q.

Onto Function or Surjective function:

A function where each element of set Q has a corresponding pre-image in set P.

One-one correspondence or Bijective function:

Each discrete element of Q has a pre-image in P, and the function f matches each element of P with a discrete element of Q.