The number of symmetric relations defined on the set ${1, 2, 3, 4}$ which are not reflexive is ______.

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answer is 960.

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Detailed Solution

Then number of symmetric relation which are not reflexive
$= 2^{\frac{n (n + 1)}{2}} - 2^{- \frac{n (n - 1)}{2}} \Rightarrow 2^{10} - 2^{6} \Rightarrow 1024 - 64 = 960$

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