Relations and Functions | Class 12 Mathematics Notes

1.1 Introduction

This section revisits the foundational concepts of relations and functions introduced in Class XI, emphasizing the notions of domain, co-domain, and range. The term 'relation' in mathematics is inspired by its English meaning, where two objects or quantities are related if there exists a recognizable connection between them. For example, consider two sets: A, the set of Class XII students in a school, and B, the set of Class XI students of the same school. Several relations from A to B can be defined, such as 'a is brother of b', 'a is sister of b', 'age of a is greater than age of b', 'total marks obtained by a is less than that of b', or 'a lives in the same locality as b'. Mathematically, a relation R from A to B is defined as any subset of the Cartesian product A × B. If (a, b) ∈ R, we say 'a is related to b' under relation R and denote it as aRb. Unlike everyday language, in mathematics, the existence of a relation does not necessarily require a recognizable connection. Functions are special types of relations where each element of the domain is related to exactly one element of the co-domain. This chapter aims to explore various types of relations and functions, including composition and invertibility, as well as binary operations.

📊 Diagram: Lejeune Dirichlet (1805-1859)

🔗 Connection: This introduction sets the stage for studying different types of relations in the next section, including empty, universal, reflexive, symmetric, and transitive relations.