Скачать или смотреть Class 12 Maths | Chapter 1 | Relations & Functions | Exercise 1.2 | Question 9

In this video you will get a detailed solution for question 9 of exercise 1.2 of chapter 1 Relations & Functions.

Dive into the world of mathematics with our detailed walkthrough of Exercise 1.2, question 9 from the Class 12 Maths curriculum. We explore various relations and determine their reflexivity, symmetry, and transitivity. Join us as we simplify complex concepts with clear explanations and examples.

Notes for Exercise 1.2
https://1drv.ms/b/s!Aszsvt35tKzggSDTb...

Time Stamps
0:00 Intro
0:05 Question 9
0:30 Solution
3:14 Outro


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Short Notes On Relations and Functions

Definition of Relation: A relation is a subset of the Cartesian product of two sets. It pairs elements of one set with elements of another set.
Definition of Function: A function is a special type of relation where each element in the domain is associated with exactly one element in the codomain.
Types of Relations

Empty Relation: A relation where no element of the set is related to any element of another set.
Universal Relation: A relation where every element of the set is related to every element of another set.
Identity Relation: A relation where every element is related to itself.
Inverse Relation: A relation obtained by reversing the order of the elements in each pair of the original relation.

Types of Functions

One-to-One Function (Injective): A function where each element of the domain is mapped to a distinct element of the codomain.
Onto Function (Surjective): A function where every element of the codomain has a preimage in the domain.
One-to-One and Onto Function (Bijective): A function that is both injective and surjective.
Constant Function: A function where every element of the domain is mapped to the same element of the codomain.
Identity Function: A function where every element of the domain is mapped to itself.

Composition of Functions
Definition: The composition of functions is the process of applying one function to the results of another function.

Equivalence Relations

Definition: A relation that is reflexive, symmetric, and transitive.
Properties:
Reflexive: Every element is related to itself.
Symmetric: If an element a is related to an element b, then b is related to a.
Transitive: If an element a is related to b, and b is related to c, then a is related to c.
Important Keywords and Concepts
Relation: A subset of the Cartesian product of two sets.
Function: A special type of relation with a unique output for each input.
Domain: The set of all possible inputs for a function.
Codomain: The set of all possible outputs for a function.
Range: The set of all actual outputs of a function.
Injective Function (One-to-One): A function where distinct inputs have distinct outputs.
Surjective Function (Onto): A function where every element of the codomain is an output of the function.
Bijective Function (One-to-One and Onto): A function that is both injective and surjective.
Identity Function: A function where every element maps to itself.
Composition of Functions: Combining two functions to form a new function.
Inverse Function: A function that reverses the effect of the original function.