CBSE Class 12 Mathematics – Relations and Functions

Chapter Overview

This chapter focuses on relations and functions, their types, and properties. It introduces concepts such as domain, codomain, and range, and builds a foundation for types of relations (reflexive, symmetric, transitive, equivalence). Functions are discussed in terms of one-one, onto, into, many-one, composition, and invertibility. These are foundational concepts for understanding higher mathematics, calculus, and real-world modeling.

Important Keywords

• Relation: A subset of the Cartesian product of two sets.
• Function: A relation in which each element of the domain maps to one and only one element of the codomain.
• Domain: Set of all input values (first elements).
• Range: Set of all output values (images under the function).
• One-One (Injective): Each element of the codomain is mapped by at most one element of the domain.
• Onto (Surjective): Every element of the codomain is an image of some element of the domain.
• Bijective: A function that is both one-one and onto.
• Composition of Functions: Combining two functions such that the output of one becomes input to another.
• Inverse Function: Reverses the effect of the original function, defined only for bijective functions.
• Equivalence Relation: A relation that is reflexive, symmetric, and transitive.