The number of reflexive relations on ann-element set is 2n2−n

Can anybody tell me why so?

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- December 27th 2011, 10:01 PMnikhilbhrTotal no. of reflexive relations on a set of n elements
The number of reflexive relations on an

*n*-element set is 2*n*2−*n*

**Can anybody tell me why so?**

- December 27th 2011, 10:52 PMFernandoRevillaRe: Total no. of reflexive relations on a set of n elements
- December 28th 2011, 04:19 AMPlatoRe: Total no. of reflexive relations on a set of n elements
- December 28th 2011, 04:27 AMnikhilbhrRe: Total no. of reflexive relations on a set of n elements
- December 28th 2011, 04:43 AMPlatoRe: Total no. of reflexive relations on a set of n elements
- December 28th 2011, 06:35 PMnikhilbhrRe: Total no. of reflexive relations on a set of n elements
total elements in that matrix=nXn

total diagonal element=n

so obviously power set off-diagonal elements=2^(n^2-1).

But i have problem with the approach u are using .Can please how off-diagonal elements are correlated with reflexive relation..

Thanx for help. - December 29th 2011, 01:03 AMFernandoRevillaRe: Total no. of reflexive relations on a set of n elements
Denote the diagonal of with . Every reflexive relation on has the form with . But has elements, so there are reflexive relations on .

- December 29th 2011, 02:24 AMnikhilbhrRe: Total no. of reflexive relations on a set of n elements
Thank u very much for your valuable help..Now i got where was the problem.Actually R= (set of diagonal element) U B ,i havent thought of this expression