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

Last updated at Jan. 28, 2020 by Teachoo

Last updated at Jan. 28, 2020 by Teachoo

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

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Chapter 1 Class 12 Relation and Functions (Term 1)

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.