If A has 64 subsets, how many elements does A have?
Answer and explanation
Correct answer: 6
If a finite set has n elements, then its total number of subsets is 2ⁿ. The question gives 2ⁿ = 64. Since 64 = 2⁶, it follows that n = 6. Therefore, A contains 6 elements, making option B correct. For comparison, a set with 5 elements has 32 subsets, one with 7 elements has 128 subsets, and one with 8 elements has 256 subsets. These checks confirm that no other option works.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
If a finite set has n elements, then its total number of subsets is 2ⁿ. The question gives 2ⁿ = 64. Since 64 = 2⁶, it follows that n = 6. Therefore, A contains 6 elements, making option B correct. For comparison, a set with 5 elements has 32 subsets, one with 7 elements has 128 subsets, and one with 8 elements has 256 subsets. These checks confirm that no other option works.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
