Let A be the set of all 50 students of class XII in a central school. Let `f: AvecN` be a function defined by `f(x)=Rol lnu m b e rofs t u d e n tx` Show that `f` is one-one but not onto

Explanation

A is the set of all` 50` students of class` X `in a school.

No two different students of the class can have same roll number.

Therefore, `f` must be one-one.

We can assume without any loss of generality that roll numbers of students are from `1 `to` 50`. This implies that `51` in `N` is not roll number of any student of the class. so that `51` can not be image of any element of `X` under` f`. Hence, `f` is not onto.