Question:
The total number of reflexive relations on a finite set having n elements is __________.
Solution:
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 $2^{n^{2}-n}$.