Example 14
Last updated at Dec. 8, 2016 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 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
Examples
Example 1
Example 2
Example 3
Example 4
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13
Example 14 You are here
Example 15
Example 16
Example 17
Example 18
Example 19
Example 20
Example 21
Example 22
Example 23 Important
Example 24
Example 25 Important
Example 26
Example 27
Example 28
Example 29
Example 30
Example 31
Example 32
Example 33
Example 34
Example 35
Example 36
Example 37
Example 38
Example 39
Example 40
Example 41
Example 42
Example 43
Example 44
Example 45
Example 46 Important
Example 47 Important
Example 48 Important
Example 49
Example 50
Example 51
About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.