Question

The total number of reflexive relations on a finite set having n elements is __________.

Answer 1

The total number of reflexive relations on a finite set having n elements is _________.
Consider a set A with n elements
Say A ={1, 2, ....... n⁻¹, n }
out of n² elements n elements are compulsory for relation to be reflexive.
i.e (1, 1) (2, 2) (3, 3) .... (n, n)
and for remaining n² − n elements, we have choice of filling i.e either they are present or absent.
Hence, Total number of reflexive relation are $2^{n^2-n}$.