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

$496$

Explanation for the correct option:

Find the required number of subsets

We have given set $\left\{1,2,3,....9\right\}$ having $9$ elements.

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

The even number subset will be $\left\{2,4,6,8\right\}$

So, there are a total of $2^4$ even subsets of $\left\{2,4,6,8\right\}$ possible.

$\therefore$The required number of subsets $=$(The total number of subsets) $-$ (The number of subsets having only even numbers)
$$\begin{gathered} =2^9-2^4 \\ =512-16 \\ =496 \end{gathered}$$

Hence, option (C), $496$ is the correct answer.