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Example 7 Let A be the set of all 50 students of Class X in a school. Let f: A → N be function defined by f(x) = roll number of the student x. Show that f is one-one but not onto. f(x) = Roll number of student x One-One f (x1) = roll number of student x1 f (x2) = roll number of student x2 Putting f(x1) = f(x2) Roll number of student x1 = roll number of student x2 Since no two students of a class can have same roll number, ∴ x1 = x2. So, f is one-one Onto f: A → N f(x) = Roll number of student x 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, Thus, there is no pre-image of 51 , Hence, f is not onto.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.