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Question

If A={1,2,3}, then number of reflexive relations that can be defined on A is

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Solution

A={1,2,3}
We know that for a reflexive relation (a,a)R aA
So, these three (1,1),(2,2),(3,3) elements should always be present for relation to be reflexive.
Now, total number elements in n(A×A)=9
Total ordered pairs =9
Among them 3 should be there for reflexive relation.
From remaining 6 elements, No of ways in which elements can be selected = all possible selections from 6 distinct elements
=6C0+6C1+...+6C6=26=64
So, 64 reflexive relations can be defined on A.

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