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  4. Let S = 1, 2, 3, ……10 . The number of subsets of S containing only odd numbers is

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Q. Let $S = \{1, 2, 3, ……10\}$. The number of subsets of $S$ containing only odd numbers is

KEAMKEAM 2017Sets

Solution:

Given set is $\{1,2,3, \ldots, 10\}$
The odd numbers in the given set are $1,3,5,7,9$.
$\therefore $ The number of subsets of $5$ containing only number $=2^{5}-1$
$=32-1=31$