If the power set of a set has 32 elements, how many elements does the original set have?
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Answer and explanation
Correct answer: 5
If a finite set has n elements, its power set has 2ⁿ elements because each original element may either be included or excluded from a subset. Here 2ⁿ = 32. Since 32 = 2⁵, we obtain n = 5. Thus the original set contains five elements, so option B is correct. The other numerical choices do not satisfy 2ⁿ = 32.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
If a finite set has n elements, its power set has 2ⁿ elements because each original element may either be included or excluded from a subset. Here 2ⁿ = 32. Since 32 = 2⁵, we obtain n = 5. Thus the original set contains five elements, so option B is correct. The other numerical choices do not satisfy 2ⁿ = 32.
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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