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


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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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.