Example 14 - Chapter 1 Class 12 Relation and Functions (Term 1)

Last updated at Jan. 28, 2020 by Teachoo

Example 14 - Show that one-one function f:{1, 2, 3} -> {1,2,3} is onto

Example 14 - Chapter 1 Class 12 Relation and Functions - Part 2

Example 14 - Chapter 1 Class 12 Relation and Functions - Part 3

Example 14 - Chapter 1 Class 12 Relation and Functions - Part 4

Solve all your doubts with Teachoo Black (new monthly pack available now!)

Join Teachoo Black

Next: Example 15 →

Transcript

Example 14 (Method 1) Show that an one-one function f : {1, 2, 3} → {1, 2, 3} must be onto. Since f is one-one Hence every element 1,2,3 has either of image 1,2,3 and that image is unique Note that in each case, every image has a corresponding element Hence, one-one function f : {1, 2, 3} → {1, 2, 3} is onto. Example 14 (Method 2) Show that an one-one function f : {1, 2, 3} → {1, 2, 3} must be onto. Suppose f is not onto, So, atleast one image will not have a pre=image Let 3 not have a pre-image Then, Suppose 1 has image 1, & 2 has image 2, & let 3 have image 2 But 2 & 3 have the same image 2, Hence, f is not one-one. But, given that f is one-one, So, f must be onto

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular