1.1 Introduction

Screen Readable NCERT Class 12 Mathematics Textbook for Blind and Visually Impaired Students prepaired by Professor T K Bansal.

Recall that the notion of relations and functions, domain, co-domain and range have been introduced to you in Class 11, along with different types of specific real valued functions and their graphs. The concept of the term ‘relation’ in mathematics has been drawn from the meaning of relation in English language, according to which, two objects or quantities are related to each other, if there is a recognisable connection or link between the two objects, or quantities.

Let,


A be the set of students of Class 12 of a school, and


B be the set of students of Class 11 of the same school.

Then some of the examples of relations from A to B are


(i) {(a, b) ∈ A × B: a is brother of b},


(ii) {(a, b) ∈ A × B: a is sister of b},


(iii) {(a, b) ∈ A × B: age of a is greater than age of b},


(iv) {(a, b) ∈ A × B: total marks obtained by a in the final examination is less than the total marks obtained by b in the final examination},


(v) {(a, b) ∈ A × B: a lives in the same locality as b}.

However, abstracting from this, we define mathematically a relation R from A to B as an arbitrary subset of A × B.

If (a, b) ∈ R, we say that a is related to b under the relation R and we write as a R b.


In general, (a, b) ∈ R, we do not bother whether there is a recognisable connection or link between a and b.

As seen in Class 11, functions are special kind of relations.

In this chapter, we will study different types of relations and functions, composition of functions, invertible functions and binary operations.