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.
Give reasons to support your answer to (i).
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.
Give reasons to support your answer to (i).
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For a function to be bijective, both injectivity and surjectivity must hold. In this case, the function fails to be surjective due to the infinite codomain.
Updated On: Jun 21, 2025
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Solution and Explanation
From part (i), the function is injective because each student has a unique roll number, which means no two students share the same roll number. However, the function is not surjective because the set of natural numbers is infinite, and not every natural number is a roll number for the students in the class. Since the function is not surjective, it cannot be bijective.
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