If \(A=\{1,2,3,4\}\), how many times does the whole set \(A\) appear in \(\mathcal{P}(A)\)?
Answer and explanation
Correct answer: 1
The power set \(\mathcal{P}(A)\) is the set of all distinct subsets of \(A\). The original set \(A\) is itself a subset of \(A\), so it is included in the power set exactly once. The number \(2^4=16\) represents the total number of different subsets, not the number of times one particular subset is repeated. Therefore, the whole set appears once.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The power set \(\mathcal{P}(A)\) is the set of all distinct subsets of \(A\). The original set \(A\) is itself a subset of \(A\), so it is included in the power set exactly once. The number \(2^4=16\) represents the total number of different subsets, not the number of times one particular subset is repeated. Therefore, the whole set appears once.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
