Question

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

• A. \(324\)
• B. \(396\)
• C. \(496\)
• D. \(512\)

Hint:

Use complement: Total subsets \(-\) subsets containing no odd numbers.

Answer 1

The Correct Option is C

Step 1: Find total number of subsets.
Set has \(9\) elements, total subsets:
\[ 2^9=512 \]
Step 2: Subsets with no odd numbers (only even numbers).
Even numbers in set: \(\{2,4,6,8\}\)
Number of even numbers \(=4\).
Subsets formed only from evens:
\[ 2^4=16 \]
Step 3: Required subsets.
Subsets with at least one odd number:
\[ 512-16=496 \]
Final Answer:
\[ \boxed{496} \]