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What is the possible number of reflexive relation on a set of $5$ elements?

  1. $2^{10}$
  2. $2^{15}$
  3. $2^{20}$
  4. $2^{25}$
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2 Answers

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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.

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