KCET · Maths · Sets and Relations
If \(A=\{1,2,3, \ldots, 10\}\), then number of subsets of \(A\) containing only odd numbers is
- A 31
- B 27
- C 32
- D 30
Answer & Solution
Correct Answer
(A) 31
Step-by-step Solution
Detailed explanation
Given, \(A=\{1,2,3, \ldots, 10\}\)
Set \(A\) containing only odd number \(=\{1,3,5,7,9\}\) Number of subsets \(=2^5\)
[it contains empty set also]
The required number of subsets of \(A\) containing only odd number \(=2^5-1\)
\[
=32-1=31
\]
Set \(A\) containing only odd number \(=\{1,3,5,7,9\}\) Number of subsets \(=2^5\)
[it contains empty set also]
The required number of subsets of \(A\) containing only odd number \(=2^5-1\)
\[
=32-1=31
\]
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