If the power set P(A) has 32 elements, how many elements are in the original set A?
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Answer and explanation
Correct answer: 5
If the original set A has n elements, then its power set has 2^n elements. The question gives 2^n = 32. Since 32 = 2^5, it follows that n = 5. Therefore, the original set A contains five elements. Choosing 4 would give only 16 subsets, while choosing 6 would give 64 subsets. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
If the original set A has n elements, then its power set has 2^n elements. The question gives 2^n = 32. Since 32 = 2^5, it follows that n = 5. Therefore, the original set A contains five elements. Choosing 4 would give only 16 subsets, while choosing 6 would give 64 subsets. Hence 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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