Def. : A relation 'R' on a set 'A' is called non- reflexive relation. If it is neither reflexive nor Irreflexive.
Representing relations in an $n\times n$ matrix
Total no. relations: $2^{n^2}$
Total no. of Reflexive Relations: $2^{n(n-1)}$
Total no. of Irreflexive Relations: $2^{n(n-1)}$
So total no. of Non-reflexive relation according to the def. should be
= Total no. relations - (Total no. of Reflexive Relations + Total no. of Irreflexive Relations)
$= 2^{n^2} - (2^{n(n-1)} + 2^{n(n-1)})$
$= 2^{n^2} - 2^{n(n-1) + 1}$
But I searched the internet and find total no. of Non-reflexive relation $= 2^{n^2} - 2^{n(n-1)}$
I didn't understand please help what's wrong?
Your calculations are correct. Can you provide the source of the answer you found ?