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 is both injective and surjective. 
1. Injective: A function is injective (one-to-one) if different elements in the domain map to different elements in the codomain. In this case, since each student has a unique roll number, no two students will have the same roll number. 
Hence, \( f \) is injective. 
2. Surjective: A function is surjective (onto) if every element in the codomain has a preimage in the domain. 
Here, since the set \( A \) has 30 students, and the natural numbers are infinite, \( f \) is not surjective because not every natural number corresponds to a roll number of a student. 
Therefore, \( f \) is not surjective. Thus, \( f \) is not bijective.