Question

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

• A. $324$
• B. $396$
• C. $496$
• D. $512$

Answer 1

The correct option is C $496$

The given subsets $\{1,2,3,....9\}$

So, there are total $2^9$ subsets of $\{1,2,3,...9\}$

The even subsets will be $\{2,4,6,8\}$

So, there are $2^4$ even subsets of $\{2,4,6,8\}$

The required number of a subset $=$ The total number of subsets $-$ The number of subsets having only even numbers.

$\therefore$ The required subsets $=2^9-2^4$

$=512-16$

$=496$