The number of reflexive relations from set $A$ to $A$ , defined as $A = {x : x is a letter of word COOL}$ , is

56

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64

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32

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128

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Solution

The correct option is B $64$
$A = {C, O, L}$
Let $k = n (A) = 3$
Now, number of reflexive relations will be $= 2^{k (k - 1)}$
$= 2^{3 \times 2} = 2^{6} = 64$

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