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Let $\mathrm{X}$ be any non-empty set containing $\mathrm{n}$ elements. Then what is the number of relations on $\mathrm{X}$ ?
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Verified Answer
The correct answer is:
$2^{\mathrm{n}^{2}}$
Number of elements in $\mathrm{X}$, is $\mathrm{n}$, then the number of relations on $\mathrm{X}$ means, number of elements of cartesian product $\mathrm{X} \times \mathrm{X}$
Since, $n(X)=n$ So, $\mathrm{n}(\mathrm{X} \times \mathrm{X})=\mathrm{n}, \mathrm{n}$
then the total number of relations is $2^{
\mathrm{n} \mathrm{n}}=2^{\mathrm{n}^{2}}$
Since, $n(X)=n$ So, $\mathrm{n}(\mathrm{X} \times \mathrm{X})=\mathrm{n}, \mathrm{n}$
then the total number of relations is $2^{
\mathrm{n} \mathrm{n}}=2^{\mathrm{n}^{2}}$
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