Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

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Chapter 1 Class 12 Relation and Functions

Serial order wise

Last updated at May 29, 2023 by Teachoo

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