A set contains $(2n+1)$ elements.The number of subsets of this set containing more than $n$ elements is equal to $2^{2n}$. How is this possible, if the number of subsets of a set is $2^{n}$.
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1$\begingroup$ You may be confused about the letter $n$. The number of subsets of a set of size $m$ is $2^m$. The number of subsets of a set of size $2n+1$ is $2^{2n+1}$; the number containing more than $n$ elements is half that, by joriki's answer. $\endgroup$– Patrick StevensCommented Apr 7, 2016 at 8:08
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$\begingroup$ you are right sir..thanks $\endgroup$– T.NoorCommented Apr 7, 2016 at 8:13
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Consider a subset of a set of $2n+1$ elements and its complement. Exactly one of the two has more than $n$ elements. Since the total number of subsets is $2^{2n+1}$ and they come in complementary pairs, exactly half, i.e. $2^{2n}$, have more than $n$ elements.
