Question

Let A be the set of 30 students of class XII in a school. Let f : A -> N, N is a set of natural numbers such that function f(x) = Roll Number of student x.
On the basis of the given information, answer the followingIs \( f \) a bijective function?

Hint:

A function is bijective if it is both injective (one-to-one) and surjective (onto). In this case, the function is injective but not surjective.

Answer 1

A function is bijective if it satisfies both injectivity and surjectivity.
1. Injective: A function is injective (one-to-one) when distinct domain elements map to distinct codomain elements. In this scenario, each student possesses a unique roll number, ensuring that no two students share the same roll number. 
Consequently, \( f \) is injective. 
2. Surjective: A function is surjective (onto) if every element in the codomain has at least one corresponding element in the domain (its preimage). 
Given that set \( A \) comprises 30 students and the set of natural numbers is infinite, \( f \) is not surjective because not all natural numbers are assigned as roll numbers to students. 
Therefore, \( f \) is not surjective. As a result, \( f \) is not bijective.