Dark Mode

Lakshman Patel RJIT
asked
in Set Theory & Algebra
Mar 31, 2020
retagged
Oct 23, 2020
by Krithiga2101

318 views
1 vote

Similar question: https://gateoverflow.in/333214/gate2020-cs-17

So, the total number of relations over a set of $n$ elements is: $2^{n^{2}}$

No. of elements excluding the diagonal elements: $n^{2}-n$

These elements can either be chosen or not chosen. (we have to chose diagonal elements.So only 1 way to chose them all)

So, the total number of reflexive relations possible over a set of $n$ elements is: $2\times2\times....(n^{2}-n)times$ $=$ $2^{n^{2}-n}$

For this question, $n=5$ $\Rightarrow$ answer is : $2^{25-5}=2^{20}$

Option C is correct.