Relations and Functions

In mathematics, we often deal with sets of numbers or objects and the ways they are connected. Two important concepts that help us describe these connections are relations and functions.

• A relation is simply a connection between two sets of objects. Think of it as a rule that pairs elements from one set with elements from another set.
  For example, the relationship “is greater than” pairs numbers like 5 and 3 because 5 is greater than 3.

• A function, on the other hand, is a special kind of relation. In a function, each element from the first set (called the domain) is connected to exactly one unique element in the second set (called the range).
  For instance, if you assign a name to each roll number in a class, that is a function because each roll number is paired with one unique name.

This article will cover the fundamental concepts of functions and relations in mathematics, from basic to advanced topics. It will also explore their real-life applications, practice questions and quizzes, and special section created for programmars.

Relations in Maths

This section introduces the concept of relations, their representation, types, properties, and how sets interact through relations.

• Introduction to Relations in Maths
• Cartesian Product of Sets
• Representation of Relations
• Domain and Range of a Relation
• Types of Relations
  • Reflexive Relation
  • Symmetric Relation
  • Antisymmetric Relatio
  • Transitive Relation
  • Equivalence Relation
  • Binary Relation
  • Partial Order Relation
  • Inverse Relation

• Composition of Relations

Functions in Maths

Learn what functions are, their types, properties, and how they map inputs to outputs with real-life examples and mathematical operations.

• Introduction to Functions
• Domain and Range of a Function
• Types of Functions
  • One-to-One (Injective) Function
  • Onto (Surjective) Function
  • Bijective Function
  • Many-One Function

• Other Types of Functions
  • Constant Function
  • Identity Function
  • Polynomial Function
  • Rational Function
  • Trigonometric Function
  • Exponential Function
  • Logarithmic Function
  • Piecewise Functions
  • Even and Odd Functions
  • Periodic Functions
  • Real-Valued Functions: [Algebra of Real Functions]
• Composition of Functions
• Inverse of a Function

Other Important Topics

Explore key differences between relations and functions and see how they appear in real-world situations.

• Difference between Relation and Function
• Real-Life Examples of Relations
• Real-Life Applications of Functions

Practice for Relations and Functions

Practice and test your understanding with quizzes and problems on relations and functions.

• Question on Functions
• Relation and Functions – Quiz

Program for Relations and Functions

Solve programming tasks that check properties like reflexivity, symmetry, transitivity, and equivalence in relations.

• Program to Check Reflexive Relation
• Program to Check Transitive Relation
• Program to Check Symmetric Relation
• Program to Check Anti-Symmetric Relation
• Program to Check Equivalence Relations