Find the number of binary operations on the set ${a, b}$

10

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16

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20

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8

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Solution

The correct option is C $16$
Considering 'n' elements in a set, the no. of binary operations on that set will be
$= n^{n^{2}}$
Applying this concept to the above set gives us
$= 2^{2^{2}}$ ................... $∵ n = 2$
$= 2^{4}$
$= 16$ .

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