The number of subsets of {1, 2, 3, ldots, 9} | vedclass

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(C) The total number of subsets of the set $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ is $2^n$,where $n=9$. Total subsets $= 2^9 = 512$. We want to find the

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$496$

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(C) The total number of subsets of the set $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ is $2^n$,where $n=9$. Total subsets $= 2^9 = 512$. We want to find the number of subsets that contain at least one odd number. It is easier to calculate the complement: the number of subsets that contain $NO$ odd numbers. $A$ subset contains no odd numbers if and only if all its elements are even. The even numbers in the set are $\{2, 4, 6, 8\}$. The number of subsets formed using only these even numbers is $2^4 = 16$. These $16$ subsets include the empty set $\emptyset$. Therefore,the number of subsets containing at least one odd number is Total subsets $-$ Subsets with only even numbers. Required number $= 512 - 16 = 496$.

The number of subsets of $\{1, 2, 3, \ldots, 9\}$ containing at least one odd number is

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