If $A = {a, b, c},$ then the number of reflexive relations that can be defined on $A$ is equal to

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Solution

$A = {a, b, c}$
$n (A \times A) = 9$
Reflexive relation should contain at least $(a, a), (b, b), (c, c)$
So, we can select any number of ordered pairs from the remaining $6$
$∴$ Number of reflexive relations $= 2^{6} = 64$

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1. A relation is said to be reflexive on set A if each element in A is related to itself.

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