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The number of proper subsets of a set having $n+1$ elements is
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$2^{n+1}-1$
If a set having $n$ elements then its number of subsets $=2^{n}$
$\therefore$ Numbers of proper susbets of a set having $(n+1)$ elements $=2^{n+1}-1 .$
$\therefore$ Numbers of proper susbets of a set having $(n+1)$ elements $=2^{n+1}-1 .$
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