यदि (|A|=5) है, तो (\mathcal{P}(A)) में ऐसे members कितने हैं जिनमें किसी निश्चित तत्व \(a\in A\) को रखा गया है और cardinality odd है?
If (|A|=5), how many members of (\mathcal{P}(A)) contain a fixed element \(a\in A\) and have odd cardinality?
Explanation opens after your attempt
Correct Answer
B. (8)
Concept
After fixing (a), an even number of elements must be chosen from the remaining (4) elements for odd cardinality. The number of such choices is \(2^{4-1}=8\).
Why this answer is correct
The correct answer is B. (8). After fixing (a), an even number of elements must be chosen from the remaining (4) elements for odd cardinality. The number of such choices is \(2^{4-1}=8\).
Exam Tip
(a) fixed होने पर odd cardinality के लिए बाकी (4) तत्वों में even संख्या चुननी होगी। ऐसे choices \(2^{4-1}=8\) हैं।
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