Let A be the set of all 50 students of class X in a school. Let `f : A rarr N`
be function defined by f(x) = roll numbers of the student x. Show that
f is one-one but not onto

Explanation

No two different students of the class can have same roll number.
:., .f. must be oneone. 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 cannot be image of any element of .X. under .f.. Hence, .f. is not.onto.