The total number of reflexive relations on a finite set having n elements is
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, ……. n1n }

out of n2 elements n elements are compulsory for relation to be reflexive.

i.e  (1, 1) (2, 2) (3, 3) …. (nn)

and for remaining n− n elements, we have choice of filling i.e either they are present or absent.

Hence, Total number of reflexive relation are $2^{n^{2}-n}$.

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