Question:
The number of subsets of \( \{1, 2, 3, \ldots, 9\} \) containing at least one odd number is
The number of subsets of \( \{1, 2, 3, \ldots, 9\} \) containing at least one odd number is
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"At least one" problems are often solved by: Total - None.
Updated On: Apr 10, 2026
- 324
- 396
- 496
- 512
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The Correct Option is C
Solution and Explanation
Step 1: Total Subsets
Total subsets of a set with 9 elements = $2^{9} = 512$.
Step 2: Subsets with NO Odd Numbers
Odd numbers: $\{1, 3, 5, 7, 9\}$ (5 numbers). Even numbers: $\{2, 4, 6, 8\}$ (4 numbers).
Subsets containing only even numbers = $2^{4} = 16$.
Step 3: Calculation
Required subsets = Total subsets - Subsets with only even numbers.
$512 - 16 = 496$.
Final Answer: (c)
Total subsets of a set with 9 elements = $2^{9} = 512$.
Step 2: Subsets with NO Odd Numbers
Odd numbers: $\{1, 3, 5, 7, 9\}$ (5 numbers). Even numbers: $\{2, 4, 6, 8\}$ (4 numbers).
Subsets containing only even numbers = $2^{4} = 16$.
Step 3: Calculation
Required subsets = Total subsets - Subsets with only even numbers.
$512 - 16 = 496$.
Final Answer: (c)
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