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  1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise
  3. Examples

    Example 1

    Example 2

    Example 3

    Example 4 Important

    Example 5

    Example 6 Important

    Example 7

    Example 8

    Example 9

    Example 10

    Example 11 Important

    Example 12 Important

    Example 13 Important

    Example 14 Important You are here

    Example 15 Not in Syllabus - CBSE Exams 2021

    Example 16 Not in Syllabus - CBSE Exams 2021

    Example 17 Not in Syllabus - CBSE Exams 2021

    Example 18 Important Not in Syllabus - CBSE Exams 2021

    Example 19 Important Not in Syllabus - CBSE Exams 2021

    Example 20 Not in Syllabus - CBSE Exams 2021

    Example 21 Not in Syllabus - CBSE Exams 2021

    Example 22 Not in Syllabus - CBSE Exams 2021

    Example 23 Important Not in Syllabus - CBSE Exams 2021

    Example 24 Not in Syllabus - CBSE Exams 2021

    Example 25 Important Not in Syllabus - CBSE Exams 2021

    Example 26 Not in Syllabus - CBSE Exams 2021

    Example 27 Important Not in Syllabus - CBSE Exams 2021

    Example 28 Not in Syllabus - CBSE Exams 2021

    Example 29 Not in Syllabus - CBSE Exams 2021

    Example 30 Not in Syllabus - CBSE Exams 2021

    Example 31 Not in Syllabus - CBSE Exams 2021

    Example 32 Not in Syllabus - CBSE Exams 2021

    Example 33 Not in Syllabus - CBSE Exams 2021

    Example 34 Not in Syllabus - CBSE Exams 2021

    Example 35 Not in Syllabus - CBSE Exams 2021

    Example 36 Not in Syllabus - CBSE Exams 2021

    Example 37 Not in Syllabus - CBSE Exams 2021

    Example 38 Not in Syllabus - CBSE Exams 2021

    Example 39 Not in Syllabus - CBSE Exams 2021

    Example 40 Not in Syllabus - CBSE Exams 2021

    Example 41 Important

    Example 42 Important

    Example 43 Important

    Example 44

    Example 45 Important Not in Syllabus - CBSE Exams 2021

    Example 46 Important

    Example 47 Important

    Example 48 Important

    Example 49

    Example 50

    Example 51 Important


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

Examples

Example 1

Example 2

Example 3

Example 4 Important

Example 5

Example 6 Important

Example 7

Example 8

Example 9

Example 10

Example 11 Important

Example 12 Important

Example 13 Important

Example 14 Important You are here

Example 15 Not in Syllabus - CBSE Exams 2021

Example 16 Not in Syllabus - CBSE Exams 2021

Example 17 Not in Syllabus - CBSE Exams 2021

Example 18 Important Not in Syllabus - CBSE Exams 2021

Example 19 Important Not in Syllabus - CBSE Exams 2021

Example 20 Not in Syllabus - CBSE Exams 2021

Example 21 Not in Syllabus - CBSE Exams 2021

Example 22 Not in Syllabus - CBSE Exams 2021

Example 23 Important Not in Syllabus - CBSE Exams 2021

Example 24 Not in Syllabus - CBSE Exams 2021

Example 25 Important Not in Syllabus - CBSE Exams 2021

Example 26 Not in Syllabus - CBSE Exams 2021

Example 27 Important Not in Syllabus - CBSE Exams 2021

Example 28 Not in Syllabus - CBSE Exams 2021

Example 29 Not in Syllabus - CBSE Exams 2021

Example 30 Not in Syllabus - CBSE Exams 2021

Example 31 Not in Syllabus - CBSE Exams 2021

Example 32 Not in Syllabus - CBSE Exams 2021

Example 33 Not in Syllabus - CBSE Exams 2021

Example 34 Not in Syllabus - CBSE Exams 2021

Example 35 Not in Syllabus - CBSE Exams 2021

Example 36 Not in Syllabus - CBSE Exams 2021

Example 37 Not in Syllabus - CBSE Exams 2021

Example 38 Not in Syllabus - CBSE Exams 2021

Example 39 Not in Syllabus - CBSE Exams 2021

Example 40 Not in Syllabus - CBSE Exams 2021

Example 41 Important

Example 42 Important

Example 43 Important

Example 44

Example 45 Important Not in Syllabus - CBSE Exams 2021

Example 46 Important

Example 47 Important

Example 48 Important

Example 49

Example 50

Example 51 Important

About the Author

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.