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?
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?
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Solution and Explanation
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.
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