Example 13 - Show that onto function f: {1, 2, 3} is always one-one

Example 13 - Chapter 1 Class 12 Relation and Functions - Part 2
Example 13 - Chapter 1 Class 12 Relation and Functions - Part 3

  1. Chapter 1 Class 12 Relation and Functions
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Transcript

Example 13 (Method 1) Show that an onto function f : {1, 2, 3} → {1, 2, 3} is always one-one. Since f is onto, all elements of {1, 2, 3} have unique pre-image. Following cases are possible Since every element 1,2,3 has either of image 1,2,3 and that image is unique f is one-one Since every element 1, 2, 3 has either of image 1, 2, 3 and that image is unique ∴ f is one-one Example 13 (Method 2) Show that an onto function f : {1, 2, 3} → {1, 2, 3} is always one-one. Suppose f is not one-one, So, atleast two elements will have the same image If 1 & 2 have same image 1, & 3 has image 3 Then, 2 has no pre-image, Hence, f is not onto. But, given that f is onto, So, f must be one-one

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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.