If a set A has 256 total subsets, how many elements does A have?
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Answer and explanation
Correct answer: 8
If a finite set has n elements, then its total number of subsets, including the empty set and the set itself, is 2^n. Here 2^n = 256. Since 256 = 2^8, it follows that n = 8. The neighboring choices do not work: 2^7 = 128 and 2^9 = 512. Therefore, A has exactly eight elements.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
If a finite set has n elements, then its total number of subsets, including the empty set and the set itself, is 2^n. Here 2^n = 256. Since 256 = 2^8, it follows that n = 8. The neighboring choices do not work: 2^7 = 128 and 2^9 = 512. Therefore, A has exactly eight elements.
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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