CASE STUDY CHALLENGE
Student Seating & Roll Numbers: Relations in Action
Let \( A \) be the set of 30 students of Class XII in a school. To plan seating and manage records, the teacher defines functions and relations based on the students’ roll numbers.
Let \( f: A \rightarrow N \) be a function, where \( N \) is the set of natural numbers, such that \( f(x) = \text{Roll Number of student } x \). The set of roll numbers is \( S = \{1, 2, 3, \dots, 30\} \).
Answer the following questions:
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(i) (ii) |
Is the function \( f \) bijective? Give reasons to support your answer. |
[2] |
| (iii) | (a) Let \( R \) be a relation defined on the set of roll numbers \( S \) by \( R = \{(x, y) : y = 3x, \, x, y \in S\} \). List the elements of \( R \). Is \( R \) reflexive, symmetric, and transitive? Justify.
— OR —
(b) Let \( R \) be a relation defined on the set of roll numbers \( S \) by \( R = \{(x, y) : y = x^3, \, x, y \in S\} \). List the elements of \( R \). Is \( R \) a function? Justify your answer. |
[2] |