NCERT Class 12 Maths Relations and Functions

1.1 Introduction
Recall that the notion of relations and functions, domain, co-domain and range have been introduced in Class XI 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 if there is a recognisable connection or link between the two objects or quantities. Let A be the set of students of Class XII of a school and B be the set of students of Class XI of the same school. Then some of the examples of relations from A to B are

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

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

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

      (iv) {(a, b) Î 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) Î 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) Î R, we say that a is related to b under the relation R and we write as a R b. In general, (a, b) Î R, we do not bother whether there is a recognisable

connection or link between a and b. As seen in Class XI, 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.

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