यदि \(A=\{a,b,c,d\}\), तो (\mathcal{P}(A)) में विषम संख्या वाले तत्वों के उपसमुच्चय कितने हैं?
If \(A=\{a,b,c,d\}\), how many elements of (\mathcal{P}(A)) are subsets with an odd number of elements?
Explanation opens after your attempt
Correct Answer
C. (8)
Concept
Odd-sized subsets are \(\binom{4}{1}+\binom{4}{3}=8\). For (n>0), half the subsets have odd size.
Why this answer is correct
The correct answer is C. (8). Odd-sized subsets are \(\binom{4}{1}+\binom{4}{3}=8\). For (n>0), half the subsets have odd size.
Exam Tip
विषम आकार वाले उपसमुच्चय \(\binom{4}{1}+\binom{4}{3}=8\) हैं। (n>0) में आधे उपसमुच्चय विषम आकार के होते हैं।
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