Скачать или смотреть Relations IIT JEE | By Shivam Goswami

Hello and welcome to Dream IIT 4 u online youtube channel. Here is the video tutorial for Sets and Relations, their types and operations with some common properties based on it.

What is the Relation?
It is a subset of the Cartesian product. Or simply, a bunch of points(ordered pairs).

Example: {(-2, 1), (4, 3), (7, -3)}, usually written in set notation form with curly brackets.

Types of Relations
Different types of relations are as follows:

Empty Relation
When there’s no element of set X is related or mapped to any element of X, then the relation R in A is an empty relation also called as void. I.e R= ∅.

For example,

if there are 100 mangoes in the fruit basket. There’s no possibility of finding a relation R of getting any apple in the basket. So, R is Void as it has 100 mangoes and no apples.

Universal relation
R is a relation in a set, let’s say A is a universal Relation because, in this full relation, every element of A is related to every element of A. i.e R = A × A.

It’s a full relation as every element of Set A is in Set B.

Identity Relation
If every element of set A is related to itself only, it is called Identity relation.

I={(A, A), ∈ a}.

For Example,

When we throw a dice, the outcome we get is 36. I.e (1, 1) (1, 2), (1, 3)…..(6, 6). From these, if we consider the relation(1, 1), (2, 2), (3, 3) (4, 4) (5, 5) (6, 6), it is an identity relation.

Inverse Relation
If R is a relation from set A to set B i.e R ∈ A X B. The relation R−1 = {(b,a):(a,b) ∈ R}.

For Example,

If you throw two dice if R = {(1, 2) (2, 3)}, R−1= {(2, 1) (3, 2)}. Here the domain is the Range R−1 and vice versa.

Reflexive Relation
A relation is a reflexive relation If every element of set A maps to itself. I.e for every a ∈ A,(a, a) ∈ R.

Symmetric Relation
A symmetric relation is a relation R on a set A if (a,b) ∈ R then (b, a) ∈ R, for all a &b ∈ A.

Transitive Relation
If (a,b) ∈ R, (b,c) ∈ R, then (a,c) ∈ R, for all a,b,c ∈ A and this relation in set A is transitive.

Equivalence Relation
If and only if a relation is reflexive, symmetric and transitive, it is called an equivalence relation.

How to convert a Relation into a function?
A special kind of relation(a set of ordered pairs) which follows a rule i.e every X-value should be associated with only one y-value is called a Function.
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