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

  1. Chapter 1 Class 12 Relation and Functions
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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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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.