If |P(A)| = 128, what is the value of |A|?
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Answer and explanation
Correct answer: 7
For a finite set A with n elements, the power set P(A) contains 2^n elements. Here 2^n = 128. Since 128 = 2^7, comparison of the powers gives n = 7. Thus |A| = 7. Notice that 2^6 = 64 and 2^8 = 256, so options 6 and 8 cannot satisfy the given condition. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
For a finite set A with n elements, the power set P(A) contains 2^n elements. Here 2^n = 128. Since 128 = 2^7, comparison of the powers gives n = 7. Thus |A| = 7. Notice that 2^6 = 64 and 2^8 = 256, so options 6 and 8 cannot satisfy the given condition. Therefore, option B is correct.
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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