Question

How many reflexive relations are possible in set A={a,b,c,d}​

Answer 1

There are 64 reflexive relations on A * A : Explanation : Reflexive Relation : A Relation R on A a set A is said to be Reflexive if xRx for every element of x.

Input : n = 2

Output : 4

The given set A = {1, 2}. The following

are reflexive relations on A * A :

{{1, 1), (2, 2)}

{(1, 1), (2, 2), (1, 2)}

{(1, 1), (2, 2), (1, 2), (2, 1)}

{(1, 1), (2, 2), (2, 1)}

Input : n = 3

Output : 64

The given set is {1, 2, 3}. There are

64 reflexive relations on A * A :

C++ Program to count reflexive relations

// on a set of first n natural numbers.

#include <iostream>

using namespace std;

int countReflexive(int n)

{

// Return 2^(n*n - n)

return (1 << (n*n - n));

}

int main()

{

int n = 3;

cout << countReflexive(n);

return 0;

}

Answer 2

Step-by-step explanation:

In relation and function , reflexive relation in one in which every element maps to itself

Now ,

A = { (a, a) , ( b, b) , ( c, c) , ( d, d) }

Hope it helps you....