Let `A` be the set of all 50 students of class `X I I` in a central school. Let `f: A->N` be a function defined by `f(x)=Roll\ n umber\ of\ s t u d e n t\ x` Show that `f` is one-one but not onto.

Explanation

To solve the problem, we need to show that the function \( f: A \to \mathbb{N} \) defined by \( f(x) = \) Roll number of student \( x \) is one-one (injective) but not onto (surjective).

### Step-by-Step Solution:

1. **Understanding the Function**:
- The set \( A \) consists of 50 students in class XII.
- The function \( f \) maps each student to their respective roll number, which is a unique identifier for each student.

...