Question

Let be the set of all 50 students of Class X in a school. Let ∶ → ℕ be function defined by () = roll number of the student . Show that f is one-one but not onto.

Answer 1

one-one

f (x,) = roll number of student x,

f (x) = roll number of student x,

Putting

One-One

f(x,) = f(x,)

Roll number of student x, = roll number of student x,

Since no two students of a class can have same roll number,

i* X = X

So, f is one-one

Onto

f: A → N

f(x) = Roll number of studentx

Since, there are 50 students,

roll numbers of students are from 1 to 50.

So, 51 is not a roll number of any student of the class,

Hence, f is not onto.