Example 7 - Chapter 1 Class 12 Relation and Functions
Last updated at April 16, 2024 by Teachoo
To prove one-one & onto (injective, surjective, bijective)
One One function
Onto function
One One and Onto functions (Bijective functions)
Example 7 You are here
Example 8 Important
Example 9
Example 11 Important
Misc 2
Ex 1.2, 5 Important
Ex 1.2 , 6 Important
Example 10
Ex 1.2, 1
Ex 1.2, 12 (MCQ)
Ex 1.2, 2 (i) Important
Ex 1.2, 7 (i)
Ex 1.2 , 11 (MCQ) Important
Example 12 Important
Ex 1.2 , 9
Ex 1.2 , 3
Ex 1.2 , 4
Example 25
Example 26 Important
Ex 1.2 , 10 Important
Misc 1 Important
Example 13 Important
Example 14 Important
Ex 1.2 , 8 Important
Example 22 Important
Misc 4 Important
Chapter 1 Class 12 Relation and Functions
Concept wise
- Relations - Definition
- Empty and Universal Relation
- To prove relation reflexive, transitive, symmetric and equivalent
- Finding number of relations
- Function - Definition
-
To prove one-one & onto (injective, surjective, bijective)
- Composite functions
- Composite functions and one-one onto
- Finding Inverse
- Inverse of function: Proof questions
- Binary Operations - Definition
- Whether binary commutative/associative or not
- Binary operations: Identity element
- Binary operations: Inverse
Transcript
Example 7 Let A be the set of all 50 students of Class X in a school. Let f: A → N be function defined by f(x) = roll number of the student x. Show that f is one-one but not onto. f(x) = Roll number of student x One-One f (x1) = roll number of student x1 f (x2) = roll number of student x2 Putting f(x1) = f(x2) Roll number of student x1 = roll number of student x2 Since no two students of a class can have same roll number, ∴ x1 = x2. So, f is one-one Onto f: A → N f(x) = Roll number of student x Since, there are 50 students, roll numbers of students are from 1 to 50. So, 51 is not a roll number of any student of the class, Thus, there is no pre-image of 51 , Hence, f is not onto.
