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Misc 10 - Chapter 1 Class 12 Relation and Functions
Last updated at Jan. 30, 2020 by Teachoo
Transcript
Misc 10 (Introduction) Find the number of all onto functions from the set {1, 2, 3, … , n} to itself. Taking set {1, 2, 3} Since f is onto, all elements of {1, 2, 3} have unique pre-image. Total number of one-one function = 3 × 2 × 1 = 6 Misc 10 Find the number of all onto functions from the set {1, 2, 3, … , n} to itself. Since f is onto, all elements of {1, 2, 3} have unique pre-image. Total number of onto functions = n × n –1 × n – 2 × …. × 2 × 1 = n!
To prove one-one & onto (injective, surjective, bijective)
One One function
Onto function
One One and Onto functions (Bijective functions)
Example 7
Example 8
Example 9
Example 11 Important
Misc 5
Ex 1.2, 5 Important
Ex 1.2 , 6
Example 10
Ex 1.2, 1
Ex 1.2, 12
Ex 1.2 , 2 Important
Ex 1.2 , 7
Ex 1.2 , 11
Example 12 Important
Ex 1.2 , 9
Ex 1.2 , 3
Ex 1.2 , 4
Example 50
Example 51 Important
Ex 1.2 , 10 Important
Misc. 4 Important
Example 13 Important
Example 14 Important
Ex 1.2 , 8 Important
Example 46 Important
Misc 10 Important You are here
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
About the Author
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.