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).

Hint:

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.

Answer 1

The function is injective as each student possesses a distinct roll number, precluding any shared roll numbers. However, it is not surjective because the infinite set of natural numbers does not map to every student's roll number within the class. Consequently, the function lacks bijectivity due to its non-surjective nature.