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(C) Let $n$ be the number of elements in the set. Here,$n = 4$.The total number of symmetric relations on a set with $n$ elements is given by $2^{\fra

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$960$

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(C) Let $n$ be the number of elements in the set. Here,$n = 4$.The total number of symmetric relations on a set with $n$ elements is given by $2^{\frac{n(n+1)}{2}}$.For $n = 4$,the number of symmetric relations is $2^{\frac{4(5)}{2}} = 2^{10} = 1024$.The number of symmetric relations that are also reflexive is given by $2^{\frac{n(n-1)}{2}}$.For $n = 4$,the number of symmetric and reflexive relations is $2^{\frac{4(3)}{2}} = 2^6 = 64$.The number of symmetric relations that are not reflexive is the total number of symmetric relations minus the number of symmetric and reflexive relations.Number of symmetric relations not reflexive $= 2^{10} - 2^6 = 1024 - 64 = 960$.

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

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