Let A be the set of all 50 students of class XII in a central school. Let `f: A->N` be a function defined by `f(x)`=Roll number of student `x`. Show that `f` is one-one but not onto

Explanation

f(x) = roll number of student x
`f(x_(1)) = f(x_(2)) rarr` roll number of students are same
`:.` Name of student should be same. Hence function is one - one.
`f : A rarr N`, As there are 50 students, so f(x) has 50 numbers where N contains number more than 50. Hence function is not onto.