No. of Reflexive relations

Reflexive relations
Define reflexive relations
How to find maximum no. of possible reflexive relations?
How to find total no. of possible Reflexive relations. Proof
proof maximum no of reflexive relations

Relations are related to the cartesian product of the sets .In maths, there are nine kinds of relations which are
Empty relation,
Universal relation,
Reflexive relation,
Irreflexive relation,
Symmetric relation,
Antisymmetric relation,
Transitive relation,
Equivalence relation, and
Asymmetric relation.

A relation is a reflexive relation If every element of set A related to itself. i.e for every a ∈ A, (a, a) ∈ R

OR
A relation R from a non-empty set A to a non-empty set B is a subset of the cartesian product A×B

It relates elements of one set to another set. The subset is derived by describing a relationship between the first element and the second element of the ordered pair A×B.

Domain: The set of all first elements of the ordered pairs in a relation R from a set AA to a set BB is called the domain of the relation RR.All the elements of set A is called domain of R.
Codomain: All the elements of set B are called codomain of R.
Range: All of the values that come out of a relation are called the range. Range may also be referred to as "image".: The set of all second elements of the ordered pairs in a relation R from a set A to a set B can be referred to as range of R.

Reflexive Relation

It can also be stated as a relation in a set AA is called reflexive relation if (a,a)∈R for every element a∈A.
For example,
Let 

A = {0, 1, 2, 3}A = {0, 1, 2, 3}

 and define a relation R on A as follows: 

R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}

From RR above, it is clear that
(0,0)∈R
(1,1)∈R
(2,2)∈R
(3,3)∈R
Since for every element in 

A = {0, 1, 2, 3}A = {0, 1, 2, 3}

, there exists a ordered pair (a,a)∈R,hence R is reflexive in set A.

Note: Relations are one of the means of joining sets or subsets of the cartesian product. Relations and functions are different from each other. Any relation which is reflexive, symmetric and transitive is called an equivalence relation.A function is a relation which describes that there should be only one output for each input.

Link to find maximum no of possible equivalence relations, Bell tree

Link of my 1st video complete lecture on relations

Link for Reflexive pattern trick

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