यदि \(A=\{a,b,c,d,e\}\), तो (\mathcal{P}(A)) में ऐसे कितने उपसमुच्चय हैं जिनमें (a) और (b) दोनों हैं?

If \(A=\{a,b,c,d,e\}\), how many subsets in (\mathcal{P}(A)) contain both (a) and (b)?

Explanation opens after your attempt
Correct Answer

A. (8)

Step 1

Concept

(a) and (b) are fixed, and the remaining (3) elements are free. Therefore there are \(2^3=8\) subsets.

Step 2

Why this answer is correct

The correct answer is A. (8). (a) and (b) are fixed, and the remaining (3) elements are free. Therefore there are \(2^3=8\) subsets.

Step 3

Exam Tip

(a) और (b) निश्चित हैं, बाकी (3) तत्व स्वतंत्र हैं। इसलिए \(2^3=8\) उपसमुच्चय होंगे।

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Mathematics Answer, Explanation and Revision Hints

यदि \(A=\{a,b,c,d,e\}\), तो (\mathcal{P}(A)) में ऐसे कितने उपसमुच्चय हैं जिनमें (a) और (b) दोनों हैं? / If \(A=\{a,b,c,d,e\}\), how many subsets in (\mathcal{P}(A)) contain both (a) and (b)?

Correct Answer: A. (8). Explanation: (a) और (b) निश्चित हैं, बाकी (3) तत्व स्वतंत्र हैं। इसलिए \(2^3=8\) उपसमुच्चय होंगे। / (a) and (b) are fixed, and the remaining (3) elements are free. Therefore there are \(2^3=8\) subsets.

Which concept should I revise for this Mathematics MCQ?

(a) and (b) are fixed, and the remaining (3) elements are free. Therefore there are \(2^3=8\) subsets.

What exam hint can help solve this Mathematics question?

(a) और (b) निश्चित हैं, बाकी (3) तत्व स्वतंत्र हैं। इसलिए \(2^3=8\) उपसमुच्चय होंगे।