If n(P(A)) = 8, what is n(A)?
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Answer and explanation
Correct answer: 3
For a finite set A with n(A) elements, the power set has n(P(A)) = 2ⁿ⁽ᴬ⁾ elements. Here 2ⁿ⁽ᴬ⁾ = 8. Since 8 = 2³, it follows that n(A) = 3. Option A would give only 2² = 4 subsets, while option C would give 2⁴ = 16 subsets. Therefore, option B is the unique correct answer.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
For a finite set A with n(A) elements, the power set has n(P(A)) = 2ⁿ⁽ᴬ⁾ elements. Here 2ⁿ⁽ᴬ⁾ = 8. Since 8 = 2³, it follows that n(A) = 3. Option A would give only 2² = 4 subsets, while option C would give 2⁴ = 16 subsets. Therefore, option B is the unique correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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